How do you find the asymptotes for #f(x) = (x+3)/(x-3)#?

1 Answer
May 13, 2016

Answer:

The vertical asymptote is when the denominator goes toward #0#

Explanation:

This is when #x->3#, so the vertical asymptote is #x=3#

The horizontal asymptote is when #x# becomes very large, either positive or negative. The #+3# and the #-3# make less and less of a difference, so the value goes to #x//x=1#
So the horizontal asymptote is #y=1#
graph{(x+3)/(x-3) [-12.9, 19.14, -7.67, 8.36]}