Graphs of Rational Functions

Graphs of Rational Functions - 3.5 Graphs of Rational...

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3.5: Graphs of Rational Functions Definition: If P ( x ) and Q ( x ) are polynomials, then the function F given by F ( x ) = P ( x ) Q ( x ) is called a rational function . The domain of F is the set of all real numbers except those for which Q ( x ) = 0. Example: F ( x ) = 1 x Domain = { x | x 0 } The graph does not exist when x = 0. x y 1 1 2 0.5 3 0.33 0.5 0.33 2 3 x y -1 -1 -2 -0.5 -3 -0.33 -0.5 -0.33 -2 -3 x y (1, 1) (2, .5) (.5, 2) (.33, 3) (-1, -1) (-2, -.5) (-3, -.33) (-.33, -3) (-.5, -2) (3, .33) x y horizontal asymptote vertical asymptote As x approaches the y -axis from the left , f ( x ) goes to negative infinity. As x approaches the y -axis from the right , f ( x ) goes to infinity. As x increases without bound, f ( x ) approaches the x -axis . As x decreases without bound, f ( x ) approaches the x -axis.
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V ERTICAL AND H ORIZONTAL A SYMPTOTES F ( x ) = x - 4 x - 2 Domain = { x | x 2 } x -10 -5 5 10 y 10 5 -5 -10 x = 2 y = 1 x y horizontal asymptote vertical asymptote As x approaches 2 from the left , f ( x ) goes to infinity. As x approaches 2 from the right , f ( x ) goes to negative infinity.
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