Question 959496
Undefined for {{{x=-2}}}, so that will be a horizontal asymptote.


Form into a single rational expression and look to see if any roots.


{{{(8(2x+4)-3)/(2x+4)}}}, excuse for combining steps.


{{{(16x+32-3)/(2x+4)}}}


{{{(16x+29)/(2x+4)}}}


A root at  {{{16x=-29}}}
{{{x=-29/16}}}


Notice numerator and denominator are of equal degree.  Think about what happens for x unbounded to the left and to the right.....
.... HORIZONTAL asymptote will be {{{y=(16x)/(2x)=8}}}.


How to graph:
Root at x=-29/16;
Vertical asymptote x=-2;
Horizontal asymptote y=8.
-
Check signs around the critical x values of -2 and -29/16.


{{{graph(300,300,-8,2,-5,15,8-(3/(2x+4)))}}}