9-2-1b - 2-1 Part II Graphing Rational Functions Six steps...

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Unformatted text preview: 2-1 Part II: Graphing Rational Functions Six steps to pretty good graph of a rational function x−2 f ( x) = 2 Example: x −x 1. Factor numerator and denominator as much as possible. x−2 f ( x) = x ( x − 1) 2. Draw in vertical asymptotes (at zeros of denominator). zeros of denominator are 0 and 1. 3. Draw in horizontal asymptote (if any). degree of numerator < degree of denominator, so x-axis is horizontal asymptote. f(x) 10 vertical asymptotes horizontal asymptote x -3 2 2-1 Part II p. 1 4. Draw in zeros of function (zeros of numerator). x = 2 5. Add guide points between and beyond each zero and vertical asymptote. f(-2) = -2/3 f(1/2) = 6 f(3/2) = -2/3 f(3) = 1/6 guide points x X X -3 X X X 2 zero Note: there is one zero and two vertical asymptotes for a total of three. You will need 3 + 1 = 4 guide points. You always need one more guide point than the total of zeros and vertical asymptotes. And that should be enough to ensure a good-enough graph. 2-1 Part II p. 2 6. Draw. Make sure function approaches horizontal asymptote at left and right extremities. • start at extreme left • graph must enter from close to the horizontal asymptote there • or come from + or - oo, if no horizontal asymptote • will the graph start from above the asymptote or below the asymptote? • look at the left-most guide point for the clue • you must start on that side of the asymptote • now draw the graph through the left-most "in-between" point • graph must go off-scale at vertical asymptotes • it must never cross the x-axis except at marked zeros This can all be done with almost no algebra; just draw in some asymptotes and points and draw your graph! f(x) -3 10 2 2-1 Part II p. 3 ...
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This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.

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9-2-1b - 2-1 Part II Graphing Rational Functions Six steps...

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