What is the horizontal asymptote for #y=(x^2-x-6)/(x+4)#?

1 Answer
Oct 25, 2015

Answer:

This function has an oblique asymptote #y = x-5#, a vertical asymptote #x=-4# and no horizontal asymptote.

Explanation:

#y = (x^2-x-6)/(x+4) = (x^2+4x-5x-20+14)/(x+4) = x-5+14/(x+4)#

As #x->+-oo#, #14/(x+4)->0#

So this function has an oblique asymptote #y = x-5#, a vertical asymptote #x=-4# and no horizontal asymptote.