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Section4.2 Rational Functions and Their Graphs

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Rational Functions

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Example Find the domain of the rational function.

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Example Find the domain of the rational function.

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Vertical Asymptotes of Rational Functions

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Two Graphs with Vertical Asymptotes, one without

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Example Find the vertical asymptote, if any, of the graph of the rational function.

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Example Find the vertical asymptote, if any, of the graph of the rational function.

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Example Find the vertical asymptote, if any, of the graph of the rational function.

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A graph with a hole corresponding to the denominator’s zero. Your calculator will not show the hole.

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Horizontal Asymptotes of Rational Functions

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Two Graphs with Horizontal Asymptotes, one without Notice how the horizontal asymptote intersects the graph.

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Example Find the horizontal asymptote, if any, of the graph of the rational function.

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Example Find the horizontal asymptote, if any, of the graph of the rational function.

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Using Transformations to Graph Rational Functions

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Graphs of Common Rational Functions

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Transformations of Rational Functions

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Graphing Rational Functions

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Example

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Slant Asymptotes

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Example

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Applications

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(a) (b) (c) (d)

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(a) (b) (c) (d)

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(a) (b) (c) (d)

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