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Unformatted text preview: Rational Functions Def. A rational function is a function of the form f ( x ) = p ( x ) q ( x ) where p and q are polynomial functions and q is not the zero polynomial. Domain of a rational function: Zeros of a rational function: ex. Find the domain and zeros of the rational functions. 1) f ( x ) = x 2 x 2 ± x 2) f ( x ) = 3 x x 2 + 1 3) f ( x ) = x 2 + 4 x + 3 x 2 ± 9 Vertical Asymptotes Recall the graph of f ( x ) = 1 x Def. The line x = a is a vertical asymptote (VA) of the graph of rational function f ( x ) if NOTE: A graph DOES NOT cross its vertical asymptote(s). The graph of a rational function has a vertical asymptote at the zeros of the simpli±ed denominator. ex. Find the vertical asymptote of each function. 1) f ( x ) = x + 2 x 2 ± 9 2) g ( x ) = 2 x 2 + 4 3) h ( x ) = x 2 ± 2 x x 2 ± 3 x + 2 Horizontal Asymptotes Def. The line y = L is a horizontal asymptote (HA) of the graph f ( x ) = p ( x ) q ( x ) if...
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 Spring '08
 WILLIAMSON
 Calculus, Algebra

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