Rational Functions and their Characteristics

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What is a rational function?

Back

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CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

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CCSS.HSF-IF.C.7D

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CCSS.HSF-IF.C.7D

Front

What happens when the degrees of the numerator and denominator are equal?

Back

When the degrees of the numerator and denominator are equal, the horizontal asymptote is given by the ratio of the leading coefficients.

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CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes occur at the values of x that make the denominator equal to zero, provided these values do not also make the numerator zero.

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CCSS.HSF-IF.C.7D

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What is a hole in a rational function?

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A hole occurs in the graph of a rational function at a value of x that makes both the numerator and denominator equal to zero.

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CCSS.HSF-IF.C.7D

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CCSS.HSF-IF.C.7D

Front

What is the significance of the degree of a polynomial in rational functions?

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The degree of a polynomial determines the end behavior of the rational function and the presence of horizontal and vertical asymptotes.

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CCSS.HSF-IF.C.7D

Front

Back

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CCSS.HSF-IF.C.7D

Front

How do you determine the location of holes in a rational function?

Back

To find holes, factor both the numerator and denominator, and identify common factors that cancel out.

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CCSS.HSF-IF.C.7D