How do you find vertical, horizontal and oblique asymptotes for #f(x)=(3x)/(x-8)#?

1 Answer
Oct 30, 2016

Answer:

The vertical asymptote is #x=8#
The horizontal asymptote is #y=3#
There is no oblique asymptote

Explanation:

As you cannot divide by #0#, so #x!=8#
Therefore the vertical asymptote is #x=8#

As the degree of the numerator is equal to the degree of the denominator, there is no oblique asymptote.

Limit #f(x)=(3x)/x=3#
#x->+-oo#
Therefore #y=3# is a horizontal asymptote

graph{3x/(x-8) [-65.8, 65.9, -32.9, 33]}