# Precalculus Examples

Determine if Proper or Improper
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
Find the degree of the numerator . In this case, the degree of the numerator is .
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.
Find the degree of the denominator . In this case, the degree of the denominator is .
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 .
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 greater than the degree of the denominator .
The degree of the numerator is greater than the degree of the denominator, which means that is an improper function.
Improper

Enter the email address associated with your Mathway account below and we'll send you a link to reset your password.

The email address you entered was not found in our system
The email address you entered is associated with a Facebook user
We're sorry, we were unable to process your request at this time

Step-by-step work + explanations
•    Step-by-step work
•    Detailed explanations
•    Access anywhere
Access the steps on both the Mathway website and mobile apps
$--.--/month$--.--/year (--%)