How do you find the asymptotes for #y= (7x-2) /( x^2-3x-4)#?

1 Answer
Jan 14, 2016

Answer:

The asymptotes of any expression are found by defining what happens to the expression when #x -> oo# or #x-> - oo# or when #y->oo#

Explanation:

The asymptotes of any expression are found by defining what happens to the expression when #x -> oo# or #x-> - oo# or when #y->oo#
In this case # y =(7x+2)/(x^2 - 3x - 4)# or # (7x-2)/((x-4)(x+1))#

Hence when #x ->4# or #x -> -1# then #y -> oo#. Therefore there are vertical asymptotes at #x =4# and at #x=-1#

#lim _( x-> +-oo) (7x-2)/(x^2-3x-4) = lim_(x->+-oo) 7/x =0#