Characteristics of 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 is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine the horizontal asymptote 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= leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input approaches a certain value, typically where the function is undefined.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes are found by setting the denominator of a rational function equal to zero and solving for x.

Tags

CCSS.HSF-IF.C.7D

Front

What is a slant (oblique) asymptote?

Back

A slant asymptote occurs when the degree of the numerator is one greater than the degree of the denominator.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the slant asymptote of a rational function?

Back

Perform polynomial long division of the numerator by the denominator; the quotient (ignoring the remainder) gives the equation of the slant asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of asymptotes in graphing rational functions?

Back

Asymptotes help identify the behavior of the graph, indicating where the function does not exist and guiding the overall shape of the graph.

Tags

CCSS.HSF-IF.C.7D

Front

What happens to the graph of a rational function at vertical asymptotes?

Back

The graph will approach the vertical asymptote but will never cross it, indicating a discontinuity.

Tags

CCSS.HSF-IF.C.7D