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ss_3_7

# ss_3_7 - Section 3.7 Rational Functions A rational function...

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Section 3.7 Rational Functions A rational function , R , is a function of the form R ( x )= p ( x ) q ( x ) where p ( x ) ,q ( x ) are polynomials. Example. R ( x x +1 x +2 is a rational function. Example. R ( x x 2 +3 x - 1 x 4 +3 x 2 - 2 x is a rational function. Example. f ( x x is not a rational function. Example. f ( x )=sin x is not a rational function. The domain of a rational function, f ( x p ( x ) q ( x ) , is the set of all x such that q ( x ) 6 =0. Example. The domain of r ( x x +1 x - 2 is ( -∞ , 2) (2 , ). The graph of f ( x 1 x is shown below. –10 –5 0 5 10 –3 –2 –1 1 2 3 y = 1 x The graph of f ( x 1 x - 2 is shown below. –10 –5 0 5 10 1234 y = 1 x - 2 The graph of f ( x 1 x 2 is shown below. –10 –5 0 5 10 –3 –2 –1 1 2 3 y = 1 x 2 The graph of f ( x 1 ( x - 2) 2 is shown below. 1

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0 10 20 1234 y = 1 ( x - 2) 2 The line of y = L is a horizontal asymptote of the graph of y = f ( x )i f f ( x ) L as x →∞ or if f ( x ) L as x →-∞ . Example. The line y = 0 is a horizontal asymptote of the graph of y = 1 x .
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ss_3_7 - Section 3.7 Rational Functions A rational function...

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