Domain of Rational Functions
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.

Examples
 #1: We do not want the denominator of this function to ever equal zero. The only time this would happen is when or . In general, if we set the denominator of the function equal to zero and solve the equation, we can find out what values cannot be used in the domain of the function. What is your answer?