How do you graph #f(x)=1/(x2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
There is a vertical asymptote at
Analytically:
Since there is no variable in the numerator, the degree = 0. The degree of the denominator is 1.
From the graph: graph{1/(x2) [10, 10, 5, 5]}
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To graph the function f(x) = 1/(x2), we can follow these steps:

Determine the vertical asymptote: Set the denominator (x2) equal to zero and solve for x. In this case, x = 2. So, the vertical asymptote is x = 2.

Identify any holes: Simplify the function by canceling out common factors between the numerator and denominator. If any factors cancel out, there will be a hole at that xvalue. In this case, there are no common factors to cancel out, so there are no holes.

Find the xintercept: Set f(x) equal to zero and solve for x. In this case, 1/(x2) = 0. Since the numerator is 1, there is no solution for x that makes the function equal to zero. Therefore, there is no xintercept.

Determine the yintercept: Substitute x = 0 into the function f(x) = 1/(x2) and solve for y. In this case, f(0) = 1/(02) = 1/(2) = 1/2. So, the yintercept is (0, 1/2).

Plot the points: Plot the vertical asymptote at x = 2 and the yintercept at (0, 1/2).

Determine the behavior of the function as x approaches positive and negative infinity: As x approaches positive or negative infinity, the function approaches zero. Therefore, the xaxis (y = 0) is the horizontal asymptote.

Sketch the graph: Based on the information above, draw a curve that approaches the vertical asymptote at x = 2, passes through the yintercept at (0, 1/2), and approaches the xaxis (y = 0) as x approaches positive and negative infinity.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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