Question

Find the horizontal asymptote (H.A.) and vertical asymptote(s) (V.A.) of f (x) =
(2x^2 - 2)/(x^2 + x - 2)

Answer 1

Horizontal asymptotes you look at the leading terms.

You have 2x^(2)/x^(2)
since the leading terms are the same you look at the coefficients.
We have 2/1 or 2 as the horizontal asymptote. If you took the limit at infinity you would see this as true.

Vertical asymptote you look at the domain find that the -2 and 1 are not in the domain of the function.
Thus you plug -2 into the top part of the function and 1
if you end up with 0/0 then you have a hole but if you end up with any number other than 0 at the numerator you have an vertical asymptote.

So you have an asymptote at -2 but not at 1 because 1 makes the equation 0/0.

so HA = 2
and
VA = -2