What is your question?

You have a vertical asymptote when the function "blows up" (or "blows down") to infinity (negative infinity) at a specific x value.

You have a horizontal asymptote when the function tends to a specific y value as x tends to positive or negative infinity.

So for the first one I found a vertical asymptote at x = -2 and a horizontal asymptote at y = 2.

You do the other one.

-Dan