Characteristics of Rational Functions

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What is a rational function?

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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?

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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

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How do you find vertical asymptotes?

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To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Tags

CCSS.HSF-IF.C.7D

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What is a horizontal asymptote?

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A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes for rational functions?

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For rational functions, 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

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What is a hole in a rational function?

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A hole occurs at a point where both the numerator and denominator of a rational function are zero, indicating a removable discontinuity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find holes in rational functions?

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

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of asymptotes in rational functions?

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Asymptotes indicate the behavior of the function as it approaches certain values, helping to understand limits and graphing.

Tags

CCSS.HSF-IF.C.7D

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What is the domain of a rational function?

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The domain of a rational function includes all real numbers except where the denominator is zero.

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What is the range of a rational function?

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The range of a rational function is the set of all possible output values, which can be determined by analyzing horizontal asymptotes and holes.