### Home > PC > Chapter 8 > Lesson 8.2.1 > Problem 8-79

8-79.

Find the coordinates of any holes and the equations of any asymptotes for the function *f*(*x*) =

Factor completely:

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 2*x*^{2} in the numerator and *x*^{2} in the denominator, *y* = 2 is the horizontal asymptote.