(Graphing program required for part (c).) The rational

Chapter 9, Problem 9.4.16

(choose chapter or problem)

(Graphing program required for part (c).) The rational function can be decomposed into a sum by using the following method: write as sum of a fraction and a constant find the common denominator multiply and simplify Set numerators equal 4x 2 11 5 Bx 1 A 2 3B Set x values equal 4x 5 Bx then B 5 4 Set the constants equal 211 5 A 2 3B substitute 4 for B 211 5 A 2 3(4) then A 5 1 Therefore g(x) 5 4x 2 11 x 2 3 5 1 x 2 3 1 4 4x 2 11 x 2 3 5 A 1 Bx 2 3B x 2 3 4x 2 11 x 2 3 5 A x 2 3 1 B(x 2 3) x 2 3 4x 2 11 x 2 3 5 A x 2 3 1 B which is the graph of f(x) 5 shifted to the right by three units, then shifted up by four units. See the accompanying graph. a. Use the preceding method to decompose . b. Describe the steps in transforming the function into . c. Using technology, plot the graphs of f(x) and g(x) to verify that the transformation described in part (b) is correct.