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
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.