# How do you find the vertical, horizontal or slant asymptotes for #f(x) = (8x-12)/( 4x-2)#?

##### 1 Answer

Feb 25, 2016

There is a horizontal asymptote

There is a vertical asymptote

#### Explanation:

This is the graph of

graph{(8x-12)/(4x-2) [-20, 20, -10, 10]}

First rewrite

#f(x) = frac{8x-12}{4x-2}#

#= 2-frac{4}{2x-1}#

You can see that

#lim_{x->oo} f(x) = lim_{x->oo} (2-frac{4}{2x-1})#

#= 2-0#

#= 2#

Similarly,

#lim_{x->-oo} f(x) = 2#

There is a horizontal asymptote

There is a vertical asymptote