How do you graph # f(x) = sec (pi x)#?

Question

Brooklyn Anderson · Accepted Answer

As below

#f(x) = sec (pi x)# Standard form of equation for secant function is #y = A sec(Bx - C) + D# #A = 1, B = pi, C = D = 0# #Amplitude = |A| = NONE # for Secant function Period # = (2pi) / |B| = (2pi)/pi = 2# graph{sec (pi x) [-10, 10, -5, 5]}

Zoe Austin · Answer

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1. Determine the key features of the secant function:
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1. Determine the key features of the secant function:
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1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when \To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
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1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
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1. Determine the key features of the secant function:
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1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
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1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
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1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2}To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine functionTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} +To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equalsTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + nTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zeroTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\piTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
  To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   -To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and \To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - ItTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaksTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\thetaTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks andTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta =To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughsTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs whereTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\piTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine functionTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reachesTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2}To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches itsTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} +To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum andTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\piTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$,To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $nTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2.To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. IdentifyTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ isTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is anTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the verticalTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integerTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer.To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotesTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. SoTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
  To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So,To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   -To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, forTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - VerticalTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ fTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(xTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotesTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x)To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur whereTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) =To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosineTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \secTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equalsTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\piTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. SinceTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) \To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $,To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the periodTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, theTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period ofTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the verticalTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotesTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine functionTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occurTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function isTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur atTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ xTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\piTo graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \fracTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the verticalTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2}To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotesTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} +To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes forTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + nTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n \To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \secTo graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ andTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\piTo graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ xTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi xTo graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x =To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x)To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ willTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\fracTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occurTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur atTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ xTo graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} +To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + nTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \fracTo graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n \To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $,To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2}To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n \To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $,To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ isTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, whereTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is anTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integerTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ isTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is anTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integerTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2.To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine theTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behaviorTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3.To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the functionTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. FindTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function aroundTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximumTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around theTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimumTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum valuesTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes.To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. AsTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   -To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximumTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approachesTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum valuesTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approachesTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occurTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positiveTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur whereTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive orTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negativeTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosineTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending onTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine functionTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on theTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximumTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the signTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum andTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign ofTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimumTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum valuesTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \secTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
  To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\piTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   -To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) \To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - TheTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosineTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. FindTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine functionTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find theTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function isTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the xTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-interTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-interceptsTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1,To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts byTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, andTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solvingTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimumTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum valueTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \secTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi xTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x)To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) =To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4.To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. SketchTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 \To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graphTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $.To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. HoweverTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
  To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However,To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   -To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, \To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - PlotTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\secTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\piTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotesTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi xTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes atTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)\To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ doesTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x =To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does notTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not haveTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \fracTo graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have anyTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{nTo graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-interTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-interceptsTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2}To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4.To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
  To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. ChooseTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   -To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additionalTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional pointsTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaksTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points toTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks andTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketchTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graphTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs basedTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately.To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. YouTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximumTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You canTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum andTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluateTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimumTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum valuesTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(xTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x)To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   -To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - ConnectTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ atTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the pointsTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specificTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothlyTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly toTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ xTo graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to completeTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x \To graph the function \( f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graphTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values toTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plotTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

KeepTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot moreTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mindTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more pointsTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind thatTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points andTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understandTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graphTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand theTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph willTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behaviorTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeatTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior ofTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat everyTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the functionTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function betweenTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between theTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the verticalTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2}To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5.To graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. SketchTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ unitsTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graphTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally dueTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, makingTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to theTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sureTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the periodTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to drawTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw itTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothlyTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \piTo graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothly betweenTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \pi \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothly between theTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \pi $To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothly between the verticalTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \pi $ inTo graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothly between the vertical asymptotesTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \pi $ in $ \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothly between the vertical asymptotes, consideringTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \pi $ in $ \sec(\To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothly between the vertical asymptotes, considering the behaviorTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \pi $ in $ \sec(\piTo graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothly between the vertical asymptotes, considering the behavior of theTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \pi $ in $ \sec(\pi x) \To graph \( f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothly between the vertical asymptotes, considering the behavior of the function nearTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \pi $ in $ \sec(\pi x) $.To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothly between the vertical asymptotes, considering the behavior of the function near theTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \pi $ in $ \sec(\pi x) $.To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothly between the vertical asymptotes, considering the behavior of the function near the asymptTo graph the function $ f(x) = \sec(\pi x) $, follow these steps:

1. Determine the key features of the secant function:
   - The secant function is the reciprocal of the cosine function.
   - It has vertical asymptotes where the cosine function equals zero.
   - It has peaks and troughs where the cosine function reaches its maximum and minimum values.
   
2. Identify the vertical asymptotes:
   - Vertical asymptotes occur where the cosine function equals zero. Since the period of the cosine function is $ 2\pi $, the vertical asymptotes for $ \sec(\pi x) $ will occur at $ x = \frac{n}{2} $, where $ n $ is an integer.

3. Find the maximum and minimum values:
   - The maximum and minimum values of the secant function occur where the cosine function reaches its maximum and minimum values.
   - The maximum value of the cosine function is 1, and the minimum value is -1.
   
4. Sketch the graph:
   - Plot the vertical asymptotes at $ x = \frac{n}{2} $.
   - Draw the peaks and troughs based on the maximum and minimum values.
   - Connect the points smoothly to complete the graph.

Keep in mind that the graph will repeat every $ \frac{1}{2} $ units horizontally due to the period of $ \pi $ in $ \sec(\pi x) $.To graph $ f(x) = \sec(\pi x) $, follow these steps:

1. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when $\theta = \frac{\pi}{2} + n\pi$ and $\theta = -\frac{\pi}{2} + n\pi$, where $n$ is an integer. So, for $ f(x) = \sec(\pi x) $, the vertical asymptotes occur at $ x = \frac{1}{2} + n $ and $ x = -\frac{1}{2} + n $, where $ n $ is an integer.

2. Determine the behavior of the function around the asymptotes. As $ x $ approaches these values, the function approaches positive or negative infinity depending on the sign of $ \sec(\pi x) $.

3. Find the x-intercepts by solving $ \sec(\pi x) = 0 $. However, $\sec(\pi x)$ does not have any x-intercepts.

4. Choose some additional points to sketch the graph accurately. You can evaluate $ f(x) $ at specific $ x $ values to plot more points and understand the behavior of the function between the vertical asymptotes.

5. Sketch the graph, making sure to draw it smoothly between the vertical asymptotes, considering the behavior of the function near the asymptotes and the chosen points.

By following these steps, you can graph $ f(x) = \sec(\pi x) $ accurately.