Question

How do you find the asymptotes for `f(x) = (x+3)/(x-3)`?

Answer 1

The vertical asymptote is when the denominator goes toward `0`

Explanation:

This is when `x->3`, so the vertical asymptote is `x=3`

The horizontal asymptote is when `x` becomes very large, either positive or negative. The `+3` and the `-3` make less and less of a difference, so the value goes to `x//x=1`
So the horizontal asymptote is `y=1`
graph{(x+3)/(x-3) [-12.9, 19.14, -7.67, 8.36]}