# How do you find the vertical, horizontal and slant asymptotes of: #f(x)= ( x^3-2x-3) /( x^2+2)#?

##### 1 Answer

Oct 22, 2016

There is only a slant asymptote

#### Explanation:

The domain of the function is

So there is no vertical asymptote

The degree of the numerator is

A long division gives

So the slant asymptote is

For horizontal asymptotes, we look at the limit of

limit

limit

So there is no horizontal asymptote

graph{(x^3-2*x-3)/(x^2+2) [-10, 10, -5, 5]}