Question

For the given function, find the vertical and horizontal asymptote(s) (if there are any).

f(x) = x^2+4x-3/x-6

Answer 1

Would it be x=-6 and y=0?

Answer 2

Vertical asymptote
:
What happens to f(x) as x goes to 6: f(x) approaches inf

Oblique Asymptote:

What happens to f(x) as x goes to infty:

divide (x^2+4x-3)/(x-6) using synthetic division, you will get:

x+57/(x-6)+10

So oblique asymptote is x + 10

There is no horizontal asymptote:

http://www.wolframalpha.com/input/?i=%28x%5E2%2B4x-3%29%2F%28x-6%29