Question

What is the horizontal asymptote for `y=(x^2-x-6)/(x+4)`?

Answer 1

This function has an oblique asymptote `y = x-5`, a vertical asymptote `x=-4` and no horizontal asymptote.

Explanation:

`y = (x^2-x-6)/(x+4) = (x^2+4x-5x-20+14)/(x+4) = x-5+14/(x+4)`

As `x->+-oo`, `14/(x+4)->0`

So this function has an oblique asymptote `y = x-5`, a vertical asymptote `x=-4` and no horizontal asymptote.