MA 154 Lesson 24 DelworthMA 154 Lesson 24 DelworthSection 4.5 Rational FunctionsSteps for sketching the graph of rational functions:1) Find the horizontal asymptote, if it exists. 2) Find the vertical asymptote(s), if any exist.3) Find the y-intercept, if it exists.4) Find the x-intercept(s), if any exist.5) Does the graph cross the horizontal asymptote? If the answer is yes, where does it cross?6) Sketch the function.Sketch:f (x) 2x2 2x 4x2 x 121f (x) x2 x 6x2 3x 4MA 154 Lesson 24 DelworthSection 4.5 Rational Functionsf (x) x 1x3 4x2f (x) 3x2 3x 36x2 x 2MA 154 Lesson 24 DelworthSection 4.5 Rational FunctionsSimplify and Sketch:3f (x) x2 x 6x2 3x 2f (x) x3 x2 9x 9x 1f (x) x21 x 4 x2 3x 4 x 2 MA 154 Lesson 24 DelworthSection 4.5 Rational FunctionsFind the equation of the rational function that satisfies the following conditions:Vertical asymptote: x = -5 Vertical asymptotes: x = 3, x = -2Horizontal asymptote: y = -2 Horizontal asymptote: y = 0x-intercept: 4 x-intercept: -9, f(2) = -11Vertical asymptotes: x = 5, x = -2 Vertical asymptotes: x = 4, x = -1Horizontal asymptote: y = -3 Horizontal asymptote: y = 0x-intercepts: -6, 7 x-intercept: 2Hole at x = 1 Hole at x = – 9f(5) =
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