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.

Tags

CCSS.HSF-IF.C.7D

Front

What are the x-intercepts of a function?

Back

The x-intercepts of a function are the points where the graph of the function crosses the x-axis, meaning the output (y-value) is zero.

Front

How do you find the x-intercepts of a rational function?

Back

To find the x-intercepts, set the numerator of the rational function equal to zero and solve for x.

Tags

CCSS.HSF-IF.C.7D

Front

What are asymptotes in rational functions?

Back

Asymptotes are lines that the graph of a function approaches but never touches. They can be vertical, horizontal, or oblique.

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

A vertical asymptote occurs at values of x that make the denominator of a rational function zero, leading to undefined values.

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

A horizontal asymptote describes the behavior of a function as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine horizontal asymptotes for rational functions?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What is the horizontal asymptote if the degree of the numerator is less than the degree of the denominator?

Back

The horizontal asymptote is y = 0.

Tags

CCSS.HSF-IF.C.7D

Front

What is the horizontal asymptote if the degree of the numerator is equal to the degree of the denominator?

Back

The horizontal asymptote is y = the ratio of the leading coefficients of the numerator and denominator.

Tags

CCSS.HSF-IF.C.7D

Front

What is the horizontal asymptote if the degree of the numerator is greater than the degree of the denominator?

Back

There is no horizontal asymptote; the function may have an oblique asymptote instead.

Tags

CCSS.HSF-IF.C.7D