Find the coordinates of any holes and the equations of any asymptotes for the function f(x) =
HOLES or VERTICAL ASYMPTOTES occur when the denominator = 0. In this case x = −2 is where a hole occurs because the factor divides evenly into the numerator. And x = +2 is a vertical asymptote because the factor does not divide evenly into the numerator.
Since the dominant term is 2x2 in the numerator and x2 in the denominator, y = 2 is the horizontal asymptote.