Question 978535
The function description is a bit ambiguous.  Maybe you have {{{f(x)=(4x^2-4x-8)/(2x+2)}}}.


{{{(2x^2-2x-4)/(x+2)}}}


Vertical asymptote for x=-2 and slant asymptote {{{y=2x-2}}}, based on polynomial division.  You can check for roots, for x^2-x-2=(x+1)(x-2).  The roots are x=-1 and x=2.  That might be enough to pick the correct graph of your choices.


{{{graph(300,300,-6,6,-6,6,(4x^2-4x-8)/(2x+2))}}}
Yes, this can appear to be the same as a line, but you must understand there IS an undefined point for the function which may not show on this graph here; it is a hole.