How to find the asymptotes of #f(x) = (x+2) /( 2x-5)#?

1 Answer
Jan 15, 2016

Answer:

The asymptotes can be found by looking at #lim_(x->oo)# , #lim_(x->-oo)# and #lim_(f(x)->oo#

Explanation:

The asymptotes can be found by looking at #lim_(x->oo)# , #lim_(x->-oo)# and #lim_(f(x)->oo#

Looking at the last one first, #f(x) ->oo# as the denominator approaches zero. This occurs when #2x -> 5#. This means there is a vertical asymptote at #x = 5/2#

As #x# gets very large, either negatively or positively, #(x+2)/(2x-5) -> x/(2x) -> 1/2#
Thus there is a horizontal asymptote at #y=1/2#