256 CHAPTER 4 Polynomial and Rational Functions 34. ( ) = + − + + R x x x x x 3 10 8 15 2 2 35. ( ) = − − − + R x x x x x 6 7 3 2 7 6 2 2 36. ( ) = + + − − R x x x x x 8 26 15 2 15 2 2 37. ( ) = + + + R x x x x 5 6 3 2 38. ( ) = + − + R x x x x 30 6 2 39. ( ) = − − H x x x 3 6 4 2 40. ( ) = − − H x x x 2 2 1 2 41. ( ) = − + − + F x x x x x 5 4 2 1 2 2 42. ( ) = − − + + F x x x x x 2 15 6 9 2 2 43. ( ) ( ) = + G x x x 2 2 44. ( ) ( ) = − − G x x x 2 1 2 45. ( ) = + f x x x 1 46. ( ) = + f x x x 2 9 47. ( ) = + f x x x 1 2 48. ( ) = + f x x x 2 16 2 49. ( ) = + f x x x 1 3 50. ( ) = + f x x x 2 9 3 In Problems 51–54, find a rational function that might have the given graph. (More than one answer might be possible.) 51. x x 5 22 x 5 2 y 5 1 y 23 3 3 23 52. x y 23 3 3 23 x 5 21 x 5 1 y 5 0 53. x 5 3 1 24 22 4 23 y 3 2 21 x 5 21 x 5 2 y 5 1 22 54. x 5 23 x 5 4 y 5 3 x y 215 20 210 15 25 5 10 28 10 2 4 6 8 22 24 26 Applications and Extensions 55. Probability At a fundraiser, each person in attendance is given a ball marked with a different number from 1 through x. All the balls are then placed in an urn, and a ball is chosen at random from the urn. The probability that a particular ball is selected is x 1 . So the probability that a particular ball is not chosen is − x 1 1 . Graph ( ) = − P x x 1 1 using transformations. Comment on the probability a particular ball is not chosen as x increases. 56. Waiting in Line Suppose two employees at a fast-food restaurant can serve customers at the rate of 6 customers per minute. Further suppose that customers are arriving at the restaurant at the rate of x customers per minute. The average time T, in minutes, spent waiting in line and having your order taken and filled is given by the function ( ) = − − T x x 1 6 , where < < x 0 6. Graph this function using transformations. 57. Drug Concentration The concentration C of a certain drug in a patient’s bloodstream t hours after injection is given by ( ) = + C t t t2 1 2 (a) Find the horizontal asymptote of ( ) C t . What happens to the concentration of the drug as t increases? (b) Using a graphing utility, graph ( ) = C C t . (c) Determine the time at which the concentration is highest.
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