Question

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

Answer 1

Find the domain of this function and solve the function for numbers around the restriction.

Explanation:

First of all, you know that this function has a domain restriction, since no number can be divided by zero. Therefore, find the result of `x^2-4=0`.
You'll see that, for this function, x cannot be 2 or -2. You can then solve the function for some numbers around 2 and -2 and connect them with lines. There will be 3 intervals. For example:
`f(-4)=-0.333`
`f(-3)=-0.6`

`f(-1)=0.333`
`f(0)=0`
`f(1)=-0.333`

`f(3)=0.6`
`f(4)=0.333`
graph{x/(x^2-4) [-10, 10, -5, 5]}