How do you find the vertical, horizontal or slant asymptotes for #y = (8 x^2 + x - 2)/(x^2 + x - 72)#?

1 Answer
Oct 23, 2016

Answer:

The vertical asymptotes are #x=8# and #x=-9#
and the horizontal asymptote is #y=8#

Explanation:

We start by factorising the denominator
#x^2+x-72=(x-8)(x+9)#

As we cannot divide by so #x!=8# and #x!=-9#
So the vertical asymptotes are #x=8# and #x=-9#

As the degree of the polynomial of the numerator and denominator are the same, there is no slant asymptote.

To find the horizontal asymptote, we find the limit as #x->+-oo#
We take the highest order of the polynomials

#lim y=8/1#
#x->-oo#

And
#lim y=8/1#
#x->oo#
So the horizontal asymptote is #y=8#