Question

How do you graph `f(x) =(x)/(x^2-4)`?

Answer 1

See below:

Explanation:

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:

We see that we have a higher degree in the denominator, which means we have a horizontal asymptote at `y=0`.

For vertical asymptotes, we want ot think about what makes this function undefined. Let's rewrite the expression as

`f(x)=x/((x+2)(x-2))`

We see that our expression is undefined at `x=-2` and `x=2`. These are our vertical asymptotes.

We can put this information together to get the graph

graph{x/(x^2-4) [-10, 10, -5, 5]}

Hope this helps!