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**Section 4.1 – Rational Functions and Asymptotes**

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**Graphing and Analyzing Rational Functions**

Domain Vertical Asymptotes (x = ) Horizontal Asymptotes (y = ) Holes (x, y) Intercepts Graph

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**Find the equations of the horizontal asymptotes of:**

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Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

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Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

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Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

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Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

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**Extension: The graph contains an hole at x = -3**

Note: Cancelled and eliminated Extension: The graph contains an asymptote at x = 3 Note: not eliminated

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Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

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**Extension: The graph contains a hole at x = -2**

Note: cancelled and eliminated

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Domain: Vertical Asymptotes: Horizontal Asymptotes: Holes: Intercepts:

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**Graph the rational function which has the following characteristics**

Vert Asymp at x = 1, x = -3 Horz Asymp at y = 1 Intercepts (-2, 0), (3, 0), (0, 2) Passes through (-5, 2)

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**Graph the rational function which has the following characteristics**

Vert Asymp at x = 1, x = -1 Horz Asymp at y = 0 Intercepts (0, 0) Passes through (-0.7, 1), (0.7, -1), (-2, -0.5), (2, 0.5)

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