### Home > CALC > Chapter 2 > Lesson 2.2.4 > Problem 2-100

2-100.

Let* f*(*x*) = *x*^{2} − 9, and *g*(*x*) = 2*x*^{2} − 12*x* + 18. Find all horizontal asymptotes, vertical asymptotes, and holes (if any) for

Find horizontal asymptotes by using limits as *x* → ±∞.

Find vertical asymptotes and holes by factoring and simplifying.

Even though (*x* − 3) cancels out, there remains an (*x* − 3) in the denominator. No holes, there is a vertical asymptote at *x* = 3.

Find horizontal asymptotes by using limits as *x* → ±∞.

Find vertical asymptotes and holes by factoring and simplifying.