# How do you find the Vertical, Horizontal, and Oblique Asymptote given #Q(x) =( 2x^2) / (x^2 - 5x - 6)#?

##### 1 Answer

Vertical Asymptotes : x=6 and x=-1

Horizontal asymptotes:y=2

#### Explanation:

The first step is factor the numerator and denominator

if possible .

We can factor the denominator

(x^2-5x-6=(x-6)(x+1)#

Vertical asymptote is a point to which x approaches make the

function approaches + or - infinity .

So

Set denominator as 0, solve for x.

So vertical asymtotes are x=6 and x=-1

Horizontal asymptote is the value of the function

when x approches infinity.

To find horizontal asymptote

we have to use the degree of numerator and denominator.

Here both have the same degree

y= ( leading coefficient of numerator) /(leading coefficient of denominator) is the horizontal asymptote.

If the degree of numerator > degree of the denominator , then we would get the slant asymptote.

Here no slant asymptote are there.