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**9.2 Graphing Simple Rational Functions**

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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.**

x=0 A type of rational function. Has 1 vertical asymptote and 1 horizontal asymptote. Has 2 parts called branches. (blue parts) They are symmetrical. We’ll discuss 2 different forms. 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 Left of vert. asymp. Right of vert. asymp. Domain: all real #’s except 1. Range: all real #’s except 2.

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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 p 290 from 20-29

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Factor the following completely: 1.3x 2 -8x+4 2.11x 2 -99 3.16x 3 +128 4. x 3 +2x 2 -4x-8 5.2x 2 -x-15 6.10x 3 -80 (3x-2)(x-2) 11(x+3)(x-3) 16(x+2)(x 2.

Factor the following completely: 1.3x 2 -8x+4 2.11x 2 -99 3.16x 3 +128 4. x 3 +2x 2 -4x-8 5.2x 2 -x-15 6.10x 3 -80 (3x-2)(x-2) 11(x+3)(x-3) 16(x+2)(x 2.

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