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PP Section 4.7

# PP Section 4.7 - RationalFunctions Definition A rational...

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Rational Functions

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A rational function is a function of the form R x p x q x ( ) ( ) ( ) = where p(x) and q(x) are polynomial functions and q(x) is not the zero polynomial. The domain consists of all real numbers except those for which the denominator q(x) is 0. Definition
Examples Find the domain of the following rational functions. (a) R x x x x ( ) = + + + 1 8 12 2 We need to find the places where the denominator equals  zero. ( 29 ( 29 2 6 1 ) ( + + + = x x x x R The domain is all real numbers x except -6 and -2.

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(b) R x x x ( ) = - - 4 16 2 ( 29 ( 29 4 4 4 + - - = x x x The domain is all real numbers x except -4 and 4. (c) R x x ( ) = + 5 9 2 The denominator is never zero, so the domain is all  real numbers.
Reciprocal Functions odd 1 x y = even 1 x y =

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Example We can sketch the graph of some rational functions using the graphs of the previous slide and transformations. 1 2 1 ) ( function Graph the + - = x x f To sketch the graph of f, we need to move our basic graph 2 units to the right and one unit up.
x y 1 = 1 2 1 + - = x y

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Asymptotes If as the value of | x
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PP Section 4.7 - RationalFunctions Definition A rational...

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