Question

What are the asymptotes of `y=x^2/(x^2-1)` and how do you graph the function?

Answer 1

`x^2-1` can be factorized into `(x-1)(x+1)`

Explanation:

Both `x=+1` and `x=-1` are the vertical asymptotes, as they would make the denominator `=0` and the function undefined.

As `x` gets larger (positive or negative) the function looks more and more like `x^2/x^2=1`, so `y=1` is another (horizontal) asymptote.

graph{x^2/(x^2-1) [-10, 10, -5, 5]}