# Precalculus Examples

A rational function is any function which can be written as the ratio of two polynomial functions.

is a rational function

A rational function is proper when the degree of the numerator is less than the degree of the denominator, otherwise it is improper.

Degree of numerator is less than the degree of denominator implies a proper function

Degree of numerator is greater than the degree of denominator implies an improper function

Degree of numerator is equal to the degree of denominator implies an improper function

Remove parentheses.

Identify the term with the largest exponent on the variable.

The degree is the sum of the exponents of each variable in the expression. In this case, the degree of is .

The degree is the sum of the exponents of each variable in the expression. In this case, the degree of is .

The degree is the sum of the exponents of each variable in the expression. In this case, the degree of is .

Identify the term with the largest exponent on the variable.

The degree of the polynomial is the largest exponent on the variable.

Remove parentheses.

Identify the term with the largest exponent on the variable.

Identify the term with the largest exponent on the variable.

The degree of the polynomial is the largest exponent on the variable.

The degree of the numerator is less than the degree of the denominator .

The degree of the numerator is less than the degree of the denominator, which means that is a proper function.

Proper