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9.2 Graphing Simple Rational Functions (p. 280)

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Rational Function A function of the form where p(x) & q(x) are polynomials and q(x)0.

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Hyperbola A type of rational function. Has 1 vertical asymptote and 1 horizontal asymptote. Has 2 parts called branches. (blue parts) They are symmetrical. Well discuss 2 different forms. x=0 y=0

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Hyperbola (continued) One form: Has 2 asymptotes: x=h (vert.) and y=k (horiz.) Graph 2 points on either side of the vertical asymptote. Draw the branches.

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Hyperbola (continued) Second form: Vertical asymptote: Set the denominator equal to 0 and solve for x. Horizontal asymptote: Graph 2 points on either side of the vertical asymptote. Draw the 2 branches.

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Ex: Graph State the domain & range. Vertical Asymptote: x=1 Horizontal Asymptote: y=2 x y Domain: all real #s except 1. Range: all real #s except 2. Left of vert. asymp. Right of vert. asymp.

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Ex: Graph State domain & range. Vertical asymptote: 3x+3=0 (set denominator =0) 3x=-3 x= -1 Horizontal Asymptote: x y Domain: All real #s except -1. Range: All real #s except 1/3.

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Assignment Assignment p 290 from Assignment

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