# Zeros of Rational Functions

## INTERCEPTS OF RATIONAL FUNCTIONS

A rational function will have a -intercept at , if the function is defined at zero. A rational function will not have a y-intercept if the function is not defined at zero.

Likewise, a rational function will have -intercepts at the inputs that cause the output to be zero. Since a fraction is only equal to zero when the numerator is zero, -intercepts can only occur when the numerator of the rational function is equal to zero.

#### EXAMPLE 10

##### Finding the Intercepts of a Rational Function

##### Solution

We can find the -intercept by evaluating the function at zero

The -intercepts will occur when the function is equal to zero:

This is zero when the numerator is zero.

The -intercept is , the -intercepts are and . See Figure 16.

**Figure 16**

Source: Rice University, https://openstax.org/books/college-algebra/pages/5-6-rational-functions

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