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 vertical asymptotes?

Back

Vertical asymptotes are lines x = a where a rational function approaches infinity or negative infinity as x approaches a.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b that the graph of a rational function approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes?

Back

Horizontal asymptotes can be found by comparing the degrees of the numerator and denominator polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What is a hole in a graph of a rational function?

Back

A hole occurs at a value of x where both the numerator and denominator are zero, indicating a removable discontinuity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you identify holes in a rational function?

Back

To identify holes, factor both the numerator and denominator and find common factors that can be canceled.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of the degree of the numerator and denominator?

Back

The degree of the numerator and denominator helps determine the behavior of the function, including the existence of horizontal asymptotes.

Tags

CCSS.HSF-IF.C.7D

Front

What is a slant 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 slant asymptotes?

Back

Slant asymptotes can be found using polynomial long division of the numerator by the denominator.

Tags

CCSS.HSF-IF.C.7D