Activity 10 - 2 2 x-5 x 2-1 3 Find the horizonal asymptotes...

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Activity 10 Name 2.7 Rational Functions Vertical Asymptotes occur where the denominator of a reduced rational function is 0. 1. Find the vertical asymptotes of f ( x ) = x +2 ( x - 2) x : Asymptotes at x = 2 and x = 0 2. Find the vertical asymptotes of f ( x ) = 2 x 2 +2 x - 5 x 2 - 1 : 3. Find the vertical asymptotes of f ( x ) = 2 x 3 +2 ( x - 2) x : 4. Find the vertical asymptotes of f ( x ) = ( x +2)( x - 3) x 3 - x : Horizontal Asymptotes may occur in a rational function f ( x ) = a n x n + a n - 1 x n - 1 + ··· + a 0 b m x m + b m - 1 x m - 1 + ··· + b 0 . If n > m , there are no horizontal asymptotes (the function goes to ±∞ as x → ∞ ) If n = m , there is an asymptote at a n b m . If n < m , there is an asymptote at 0. 1. Find the horizonal asymptotes of f ( x ) = x +2 ( x - 2) x : top degree =1, bottom degree=2 asymptote at 0 2. Find the horizonal asymptotes of f ( x ) = 2 x
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Unformatted text preview: 2 +2 x-5 x 2-1 : 3. Find the horizonal asymptotes of f ( x ) = 2 x 3 +2 ( x-2) x : 4. Find the horizonal asymptotes of f ( x ) = ( x +2)( x-3) x 3-x : Inclined Asymptotes occur in a rational function f ( x ) = p ( x ) qx = a n x n + a n-1 x n-1 + ··· + a b m x m + b m-1 x m-1 + ··· + b when n = m + 1. Divide p ( x ) by q ( x ) to get f ( x ) = ax + b + r ( x ) q ( x ) . 1. Find the inclined asymptote of f ( x ) = 2 x 3 +2 x 2-2 x : 2. Find the inclined asymptote of f ( x ) =-x 2 +4 x +1 : On a separate sheet of paper, plot the above functions using the asymptotes you have found....
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