CIA 4 Rational Functions Pre-Test

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Define 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.

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CCSS.HSF-IF.C.7D

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What is the horizontal asymptote of a rational function?

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The horizontal asymptote of a rational function is a horizontal line that the graph approaches as the input values (x) approach positive or negative infinity.

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CCSS.HSF-IF.C.7D

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What is an oblique asymptote?

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An oblique asymptote is a slant line that the graph of a rational function approaches as x approaches infinity or negative infinity, occurring when the degree of the numerator is one more than the degree of the denominator.

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CCSS.HSF-IF.C.7D

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CCSS.HSA.APR.D.7

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CCSS.HSA.APR.D.6

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How do you determine if a rational function has a horizontal or oblique asymptote?

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Compare the degrees of the numerator and denominator: If the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote. If the degree of the numerator is one more than the denominator, there is an oblique asymptote.

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CCSS.HSF-IF.C.7D

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CCSS.HSA.APR.D.6

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CCSS.HSA.APR.D.7

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What is the first step in simplifying a rational expression?

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Factor the numerator and the denominator completely.

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CCSS.HSA.APR.D.6

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

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A rational function is undefined when its denominator equals zero.

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CCSS.HSF-IF.C.7D