# Can there be cubic asymptotes in rational functions

1. Oct 14, 2012

### jann95

I just got this assignment for math and the question was is it possible to have a cubic asymptote in a rational function. If so explain how and where.

2. Oct 15, 2012

### HallsofIvy

Staff Emeritus
You just need a fraction in which the numerator has degree three more than the denominator. And example is $(x^4- 1)/(x+ 1)$. Dividing both numerator and denominator by x we have $(x^3- (1/x))/(1+ (1/x))$ which approaches $x^3$ as x goes to infinity or negative infinity.