428 CHAPTER 3 Polynomial and Rational Functions Concept Check If the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a) domain (b) range (c) end behavior (d) number of zeros (e) number of turning points 45. 10x7 46. -9x6 Graph each polynomial function. 47. ƒ1x2 = 1x - 2221x + 32 48. ƒ1x2 = -2x3 + 7x2 - 2x - 3 49. ƒ1x2 = 2x3 + x2 - x 50. ƒ1x2 = x4 - 3x2 + 2 51. ƒ1x2 = x4 + x3 - 3x2 - 4x - 4 52. ƒ1x2 = -2x4 + 7x3 - 4x2 - 4x Concept Check For each polynomial function, identify its graph from choices A–F. 53. ƒ1x2 = 1x - 2221x - 52 54. ƒ1x2 = -1x - 2221x - 52 55. ƒ1x2 = 1x - 2221x - 522 56. ƒ1x2 = 1x - 221x - 52 57. ƒ1x2 = -1x - 221x - 5 58. ƒ1x2 = -1x - 2221x - 522 A. 0 2 5 x y B. 0 2 5 x y C. 0 2 5 x y D. 0 2 5 x y E. 0 2 5 x y F. 2 5 0 x y Graph each polynomial function in the viewing window specified. Then approximate the real zeros to as many decimal places as the calculator will provide. 59. ƒ1x2 = x3 - 8x2 + 2x + 5; window: 3-10, 104 by 3-60, 604 60. ƒ1x2 = x4 - 4x3 - 5x2 + 14x - 15; window: 3-10, 104 by 3-60, 604 Let x = 0 represent 1990, so x = 8 represents 1998. Use a graphing calculator to do the following. (a) Graph the data points. (b) Find a quadratic function to model the data. (c) Find a cubic function to model the data. (d) Graph each function in the same viewing window as the data points. (e) Compare the two functions. Which is a better fit for the data? Solve each problem. 61. (Modeling) Medicare Beneficiary Spending Outof-pocket spending projections for a typical Medicare beneficiary as a share of his or her income are given in the table. Year Percent of Income 1998 18.6 2000 19.3 2005 21.7 2010 24.7 2015 27.5 2020 28.3 2025 28.6 Data from Urban Institute’s Analysis of Medicare Trustees’ Report.
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