A rational

function is a

function that looks like a

fraction and has a

variable in the denominator. The following are examples of rational functions:

Note that a

function such as

is not considered a rational function. Even though it is in the form of a fraction, the denominator does not contain a variable.

Whenever we are dealing with fractions, we are not allowed to have zero in the denominator. Anytime zero is in the denominator of a fraction, we have something that is undefined. So when dealing with rational functions, we have to make sure the denominator is never equal to zero.

The

domain of a function consists of the numbers we are allowed to use for the

variable in that function. So with rational functions, if there is a number that will cause the denominator of the

function to be equal to zero, we need to exclude it from our domain.