# How do you find the asymptotes for #f(x) = (x^2 - 3x)/(x^2 + 1)#?

##### 2 Answers

#### Explanation:

To find the vertical asymptotes set the denominator equal to 0 then solve for

Any other asymptotes will either be horizontal or oblique. As the degree of the polynomial on the numerator is the same as or less than the degree of the polynomial on the denominator then we will have a horizontal asymptote.

To find this see what happens when

Thus there is a horizontal asymptote along

First observation: there can be no **vertical** asymptote, as the lower part of the fraction will never be zero.

#### Explanation:

So let's see what happens if we make

The

The function *does* cross the

graph{(x^2-3x)/(x^2+1) [-46.2, 46.27, -23.1, 23.16]}