How do you graph # f(x) =(x)/(x^24)#?
See below:
Thinking about where the asymptotes of our graph are can help us get an intuition of what it looks like.
Recall that asymptotes are areas where the graph is discontinuous, and approaches said asymptotes.
Let's start with the horizontal asymptote:
For vertical asymptotes, we want ot think about what makes this function undefined. Let's rewrite the expression as
We can put this information together to get the graph
graph{x/(x^24) [10, 10, 5, 5]}
Hope this helps!
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To graph the function f(x) = x/(x^24), follow these steps:

Determine the domain of the function by finding the values of x for which the denominator (x^24) is equal to zero. In this case, x^24 = 0 when x = 2 or x = 2. So, the domain of the function is all real numbers except 2 and 2.

Find the vertical asymptotes by setting the denominator equal to zero and solving for x. In this case, x^24 = 0 when x = 2 or x = 2. Therefore, the vertical asymptotes are x = 2 and x = 2.

Determine the horizontal asymptote by analyzing the behavior of the function as x approaches positive or negative infinity. In this case, as x approaches positive or negative infinity, the function approaches zero. Hence, the horizontal asymptote is y = 0.

Find the xintercepts by setting the numerator (x) equal to zero and solving for x. In this case, x = 0 is the xintercept.

Determine the yintercept by evaluating the function at x = 0. In this case, f(0) = 0/(0^24) = 0.

Plot the vertical asymptotes, horizontal asymptote, xintercept, and yintercept on the coordinate plane.

To complete the graph, choose additional xvalues within the domain and evaluate the function to find the corresponding yvalues. Plot these points and connect them smoothly to form the graph.
Remember to label the axes and any important points on the graph.
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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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