Graphing Rational Functions

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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

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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 in a rational function?

Back

To find vertical asymptotes, 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 asymptote is a horizontal line y = b that the graph of a function approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine horizontal asymptotes for rational functions?

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 hole in a rational function?

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A hole occurs in a rational function 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 can you identify a hole in a rational function?

Back

A hole can be identified by factoring the numerator and denominator and finding common factors that cancel out.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient affects the end behavior of the function and helps determine horizontal asymptotes.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

Simplifying a rational function means reducing it to its lowest terms by canceling common factors in the numerator and denominator.

Tags

CCSS.HSA.APR.D.6

Front

What is the process for simplifying a rational expression?

Back

Factor both the numerator and denominator, cancel any common factors, and rewrite the expression.

Tags

CCSS.HSA.APR.D.6