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Section 3.5 Rational Functions and Their Graphs
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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
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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Example
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Graphing Rational Functions
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Example
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Example
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Slant Asymptotes
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Example
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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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