How do you find the Vertical, Horizontal, and Oblique Asymptote given #Q(x) =( 2x^2) / (x^2 - 5x - 6)#?
Vertical Asymptotes : x=6 and x=-1
The first step is factor the numerator and denominator
if possible .
We can factor the denominator
Vertical asymptote is a point to which x approaches make the
function approaches + or - infinity .
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.