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 the input approaches a.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes can be found by setting the denominator of the rational function equal to zero and solving 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 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

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

Tags

CCSS.HSF-IF.C.7D

Front

What is the limit of a function as x approaches negative infinity?

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The limit of a function as x approaches negative infinity is the value that the function approaches as x decreases without bound.

Front

What is the significance of the degree of the numerator and denominator in rational functions?

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

Tags

CCSS.HSF-IF.C.7D

Front

What is the relationship between the degree of the numerator and the degree of the denominator in determining horizontal asymptotes?

Back

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If they are equal, the asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

Tags

CCSS.HSF-IF.C.7D

Front

What is the process for simplifying a rational function?

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To simplify a rational function, factor both the numerator and denominator and cancel any common factors.

Tags

CCSS.HSA.APR.D.6

Front

What is the importance of identifying asymptotes in graphing rational functions?

Back

Identifying asymptotes helps in sketching the graph of the rational function, indicating where the function will not exist and its end behavior.

Tags

CCSS.HSF-IF.C.7D