3.5_bzca5e

# 3.5_bzca5e - Section 3.5 Rational Functions and Their...

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Section 3.5 Rational Functions and Their Graphs

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Rational Functions
Rational Functions are quotients of polynomial functions. This means that rational functions can ( ) be expressed as f(x)= where p and q are ( ) polynomial functions and q(x) 0. The domain of a rat p x q x ional function is the set of all real numbers except the x-values that make the denominator zero.

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Example Find the domain of the rational function. 2 16 ( ) 4 x f x x - = -
Example Find the domain of the rational function. 2 ( ) 36 x f x x = -

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Vertical Asymptotes of Rational Functions
-4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y 1 The equation f(x)= x Vertical Asymptote on the y-axis.

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2 1 The equation f(x)= Vertical Asymptote on the y-axis. x

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Two Graphs with Vertical Asymptotes, one without

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Graphing Calculator 2 f(x)= 9 x x - Input the equation as you see at left. The first graph is Connected Mode. In connected mode, the graphing calculator plots many points and connects the points with "curves." In dot mode, the graphing calculator plots the same points but does not connect them. To change the mode on the calculator press the MODE key then scroll down to the line that says Connected Dot and choose the one that you want to use.
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