The vertical asymptote is not "x cannot equal 2" it is the line x = 2.

So the slant asymptote is .

For horizontal asymptotes we find the limit of the function as x goes to plus or minus infinity. You can see for yourself that this function blows up/down at positive/negative infinity. Or you can simply use the fact that a function with a slant asymptote will never have a horizontal asymptote.

-Dan