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

graph{sec (pi x) [-10, 10, -5, 5]}

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

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

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

1To graph $f(x) = \sec(\pi x)$, follow these steps:

1. Identify the verticalTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

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

1. Identify the vertical asymptTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

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

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

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

5. Identify the vertical asymptotes byTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

6. Determine the keyTo graph $f(x) = \sec(\pi x)$, follow these steps:

7. Identify the vertical asymptotes by findingTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

8. Determine the key featuresTo graph $f(x) = \sec(\pi x)$, follow these steps:

9. Identify the vertical asymptotes by finding whereTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

10. Determine the key features ofTo graph $f(x) = \sec(\pi x)$, follow these steps:

11. Identify the vertical asymptotes by finding where theTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

12. Determine the key features of theTo graph $f(x) = \sec(\pi x)$, follow these steps:

13. Identify the vertical asymptotes by finding where the functionTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

14. Determine the key features of the secTo graph $f(x) = \sec(\pi x)$, follow these steps:

15. Identify the vertical asymptotes by finding where the function isTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

16. Determine the key features of the secantTo graph $f(x) = \sec(\pi x)$, follow these steps:

17. Identify the vertical asymptotes by finding where the function is undefinedTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

18. Determine the key features of the secant functionTo graph $f(x) = \sec(\pi x)$, follow these steps:

19. Identify the vertical asymptotes by finding where the function is undefined.To graph the function $f(x) = \sec(\pi x)$, follow these steps:

20. Determine the key features of the secant function:
    To graph $f(x) = \sec(\pi x)$, follow these steps:

21. Identify the vertical asymptotes by finding where the function is undefined. InTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

22. Determine the key features of the secant function:
    To graph $f(x) = \sec(\pi x)$, follow these steps:

23. Identify the vertical asymptotes by finding where the function is undefined. In thisTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

24. Determine the key features of the secant function:
    -To graph $f(x) = \sec(\pi x)$, follow these steps:

25. Identify the vertical asymptotes by finding where the function is undefined. In this caseTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

26. Determine the key features of the secant function:

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

27. Identify the vertical asymptotes by finding where the function is undefined. In this case,To graph the function $f(x) = \sec(\pi x)$, follow these steps:

28. Determine the key features of the secant function:

    • The secTo graph $f(x) = \sec(\pi x)$, follow these steps:

29. Identify the vertical asymptotes by finding where the function is undefined. In this case, \To graph the function $f(x) = \sec(\pi x)$, follow these steps:

30. Determine the key features of the secant function:

    • The secantTo graph $f(x) = \sec(\pi x)$, follow these steps:

31. Identify the vertical asymptotes by finding where the function is undefined. In this case, \To graph the function \( f(x) = \sec(\pi x) , follow these steps:

32. Determine the key features of the secant function:

    • The secant functionTo graph $f(x) = \sec(\pi x)$, follow these steps:

33. Identify the vertical asymptotes by finding where the function is undefined. In this case, \secTo graph the function \( f(x) = \sec(\pi x) , follow these steps:

34. Determine the key features of the secant function:

    • The secant function isTo graph $f(x) = \sec(\pi x)$, follow these steps:

35. Identify the vertical asymptotes by finding where the function is undefined. In this case, \sec(\To graph the function \( f(x) = \sec(\pi x) , follow these steps:

36. Determine the key features of the secant function:

    • The secant function is theTo graph $f(x) = \sec(\pi x)$, follow these steps:

37. Identify the vertical asymptotes by finding where the function is undefined. In this case, \sec(\thetaTo graph the function \( f(x) = \sec(\pi x) , follow these steps:

38. Determine the key features of the secant function:

    • The secant function is the reciprocalTo graph $f(x) = \sec(\pi x)$, follow these steps:

39. Identify the vertical asymptotes by finding where the function is undefined. In this case, \sec(\theta)\To graph the function \( f(x) = \sec(\pi x) , follow these steps:

40. Determine the key features of the secant function:

    • The secant function is the reciprocal ofTo graph $f(x) = \sec(\pi x)$, follow these steps:

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

42. Determine the key features of the secant function:

    • The secant function is the reciprocal of theTo graph $f(x) = \sec(\pi x)$, follow these steps:

43. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ isTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

44. Determine the key features of the secant function:

    • The secant function is the reciprocal of the cosineTo graph $f(x) = \sec(\pi x)$, follow these steps:

45. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefinedTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

46. Determine the key features of the secant function:

    • The secant function is the reciprocal of the cosine functionTo graph $f(x) = \sec(\pi x)$, follow these steps:

47. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined whenTo graph the function $f(x) = \sec(\pi x)$, follow these steps:

48. Determine the key features of the secant function:

    • The secant function is the reciprocal of the cosine function.
      To graph $f(x) = \sec(\pi x)$, follow these steps:

49. 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:

50. Determine the key features of the secant function:

    • The secant function is the reciprocal of the cosine function.
      To graph $f(x) = \sec(\pi x)$, follow these steps:

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

52. Determine the key features of the secant function:

    • The secant function is the reciprocal of the cosine function.
      -To graph $f(x) = \sec(\pi x)$, follow these steps:

53. Identify the vertical asymptotes by finding where the function is undefined. In this case, $\sec(\theta)$ is undefined when \theta = \fracTo graph the function \( f(x) = \sec(\pi x) , follow these steps:

54. Determine the key features of the secant function:

    • The secant function is the reciprocal of the cosine function.
    • It has vertical asymptTo graph $f(x) = \sec(\pi x)$, follow these steps:

55. 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:

56. Determine the key features of the secant function:

    • The secant function is the reciprocal of the cosine function.
    • It has vertical asymptotesTo graph $f(x) = \sec(\pi x)$, follow these steps:

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

58. Determine the key features of the secant function:

    • The secant function is the reciprocal of the cosine function.
    • It has vertical asymptotes whereTo graph $f(x) = \sec(\pi x)$, follow these steps:

59. 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:

60. 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:

61. 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:

62. 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:

63. 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:

64. 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:

65. 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:

66. 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:

67. 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:

68. 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:

69. 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:

70. 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:

71. 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:

72. 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:

73. 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:

74. 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:

75. 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:

76. 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:

77. 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:

78. 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:

79. 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:

80. 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:

81. 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:

82. 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:

83. 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:

84. 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:

85. 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:

86. 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:

87. 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:

88. 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:

89. 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:

90. 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:

91. 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:

92. 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:

93. 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:

94. 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:

95. 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:

96. 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:

97. 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:

98. 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:

2. 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:

2. 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:

2. 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.

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

4. 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:

5. 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.

6. Identify theTo graph $f(x) = \sec(\pi x)$, follow these steps:

7. 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:

8. 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.

9. Identify the verticalTo graph $f(x) = \sec(\pi x)$, follow these steps:

10. 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:

11. 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.

12. Identify the vertical asymptTo graph $f(x) = \sec(\pi x)$, follow these steps:

13. 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:

14. 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.

15. Identify the vertical asymptotesTo graph $f(x) = \sec(\pi x)$, follow these steps:

16. 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:

17. 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.

18. Identify the vertical asymptotes:
    To graph $f(x) = \sec(\pi x)$, follow these steps:

19. 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:

20. 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.

21. Identify the vertical asymptotes:
    -To graph $f(x) = \sec(\pi x)$, follow these steps:

22. 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:

23. 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.

24. Identify the vertical asymptotes:

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

25. 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:

26. 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.

27. Identify the vertical asymptotes:

    • Vertical asymptTo graph $f(x) = \sec(\pi x)$, follow these steps:

28. 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:

29. 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.

30. Identify the vertical asymptotes:

    • Vertical asymptotesTo graph $f(x) = \sec(\pi x)$, follow these steps:

31. 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:

32. 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.

33. Identify the vertical asymptotes:

    • Vertical asymptotes occur whereTo graph $f(x) = \sec(\pi x)$, follow these steps:

34. 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:

35. 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.

36. Identify the vertical asymptotes:

    • Vertical asymptotes occur where theTo graph $f(x) = \sec(\pi x)$, follow these steps:

37. 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:

38. 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.

39. Identify the vertical asymptotes:

    • Vertical asymptotes occur where the cosineTo graph $f(x) = \sec(\pi x)$, follow these steps:

40. 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:

41. 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.

42. Identify the vertical asymptotes:

    • Vertical asymptotes occur where the cosine function equalsTo graph $f(x) = \sec(\pi x)$, follow these steps:

43. 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:

44. 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.

45. Identify the vertical asymptotes:

    • Vertical asymptotes occur where the cosine function equals zero. SinceTo graph $f(x) = \sec(\pi x)$, follow these steps:

46. 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:

47. 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.

48. Identify the vertical asymptotes:

    • Vertical asymptotes occur where the cosine function equals zero. Since theTo graph $f(x) = \sec(\pi x)$, follow these steps:

49. 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:

50. 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.

51. 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:

52. 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:

53. 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.

54. 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:

55. 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:

56. 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.

57. 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:

58. 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:

59. 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.

60. 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:

61. 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:

62. 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.

63. 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:

64. 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:

65. 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.

66. 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:

67. 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:

68. 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.

69. 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:

70. 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:

71. 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.

72. 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:

73. 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:

74. 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.

75. 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:

76. 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:

77. 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.

78. 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:

79. 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:

80. 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.

81. 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:

82. 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:

83. 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.

84. 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:

85. 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:

86. 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.

87. 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:

88. 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:

89. 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.

90. 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:

91. 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:

92. 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.

93. 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:

94. 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:

95. 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.

96. 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:

97. 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:

98. 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.

99. 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:

100. 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:

101. 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.

102. 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:

103. 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:

104. 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.

105. 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:

106. 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:

107. 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.

108. 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:

109. 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:

110. 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.

111. 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:

112. 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:

113. 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.

114. 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:

115. 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:

116. 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.

117. 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:

118. 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:

119. 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.

120. 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:

121. 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:

122. 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.

123. 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:

124. 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:

125. 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.

126. 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:

127. 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:

128. 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.

129. 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:

130. 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:

131. 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.

132. 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:

133. 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:

134. 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.

135. 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:

136. 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:

137. 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.

138. 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:

139. 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:

140. 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.

141. 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:

142. 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:

143. 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.

144. 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:

145. 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:

146. 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.

147. 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:

148. 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:

149. 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.

150. 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:

151. 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:

152. 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.

153. 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:

154. 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:

155. 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.

156. 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:

157. 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:

158. 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.

159. 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:

160. 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.