Unit 4 Review: Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where a rational function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes of a rational function?

Back

Set the denominator of the rational function equal to zero and solve for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line y = b that the graph of a rational function approaches as x approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes of a rational function?

Back

Compare the degrees of the numerator and denominator: If the degree of the numerator is less, y=0; if equal, y=ratio of leading coefficients; if greater, no horizontal asymptote.

Front

What is partial fraction decomposition?

Back

Partial fraction decomposition is the process of expressing a rational function as a sum of simpler fractions.

Front

How do you perform partial fraction decomposition?

Back

Factor the denominator, then express the rational function as a sum of fractions with unknown coefficients, and solve for those coefficients.

Front

What is the significance of the leading coefficient in rational functions?

Back

The leading coefficient determines the end behavior of the function as x approaches infinity or negative infinity.

Front

What does it mean for a rational function to be undefined?

Back

A rational function is undefined at values of x that make the denominator equal to zero.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except for the values that make the denominator zero.