Question

How do you find the asymptotes for `(2x^2)/((-3x-1)^2)`?

Answer 1

`x=-1/3`

Explanation:

Set each factor in the denominator to `0` and solve for `x`. Since the factor, `-3x-1`, appears twice, you only have to solve for `x` in one of the factors.

`-3x-1=0`

`-3x=1`

`color(green)(|bar(ul(color(white)(a/a)x=-1/3color(white)(a/a)|)))`

If you graph the function, you can see that the `x` values approach, but never touch `x=-1/3`.

graph{(2x^2)/(-3x-1)^2 [-7.97, 7.834, -3, 4.9]}