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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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2.6 Rational Functions and Asymptotes. Rational Function Rational function can be written in the form where N(x) and D(x) are polynomials and D(x) is.

2.6 Rational Functions and Asymptotes. Rational Function Rational function can be written in the form where N(x) and D(x) are polynomials and D(x) is.

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