Graphs of Rational Functions

Front

What is a rational function?

Back

A function that can be expressed as the ratio of two polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What is the domain of a rational function?

Back

The set of all real numbers except where the denominator is zero.

Front

What is a vertical asymptote?

Back

A vertical line x = a where the function approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

A horizontal line y = b that the function approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes for rational functions?

Back

Compare the degrees of the numerator and denominator polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What happens to a rational function at its vertical asymptotes?

Back

The function approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of horizontal asymptotes?

Back

They indicate the end behavior of the function as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is the difference between vertical and horizontal asymptotes?

Back

Vertical asymptotes are related to the values of x that make the denominator zero, while horizontal asymptotes describe the behavior of the function as x approaches infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is a hole in a rational function?

Back

A point where the function is undefined due to a common factor in the numerator and denominator.

Tags

CCSS.HSF-IF.C.7D