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