372 CHAPTER 3 Polynomial and Rational Functions 17. ƒ1x2 = 1x - 124 + 2 18. ƒ1x2 = 1 31x + 324 - 3 19. ƒ1x2 = 1 21x - 222 + 4 20. ƒ1x2 = 1 31x + 123 - 3 Use an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. 21. ƒ1x2 = 5x5 + 2x3 - 3x + 4 22. ƒ1x2 = -x3 - 4x2 + 2x - 1 23. ƒ1x2 = -4x3 + 3x2 - 1 24. ƒ1x2 = 4x7 - x5 + x3 - 1 25. ƒ1x2 = 9x6 - 3x4 + x2 - 2 26. ƒ1x2 = 10x6 - x5 + 2x - 2 27. ƒ1x2 = 3 + 2x - 4x2 - 5x10 28. ƒ1x2 = 7 + 2x - 5x2 - 10x4 Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. 29. ƒ1x2 = x3 + 5x2 + 2x - 8 30. ƒ1x2 = x3 + 3x2 - 13x - 15 31. ƒ1x2 = -2x1x - 321x + 22 32. ƒ1x2 = -x1x + 121x - 12 33. ƒ1x2 = x21x - 221x + 322 34. ƒ1x2 = x21x - 521x + 321x - 12 35. ƒ1x2 = 13x - 121x + 222 36. ƒ1x2 = 14x + 321x + 222 37. ƒ1x2 = x3 + 5x2 - x - 5 38. ƒ1x2 = x3 + x2 - 36x - 36 39. ƒ1x2 = -x3 + x2 + 2x 40. ƒ1x2 = -3x4 - 5x3 + 2x2 41. ƒ1x2 = 2x31x2 - 421x - 12 42. ƒ1x2 = x21x - 3231x + 12 43. ƒ1x2 = 2x3 - 5x2 - x + 6 44. ƒ1x2 = 2x4 + x3 - 6x2 - 7x - 2 45. ƒ1x2 = 3x4 - 7x3 - 6x2 + 12x + 8 46. ƒ1x2 = x4 + 3x3 - 3x2 - 11x - 6 Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. See Example 5. 47. ƒ1x2 = 2x2 - 7x + 4; 2 and 3 48. ƒ1x2 = 3x2 - x - 4; 1 and 2 49. ƒ1x2 = -2x3 + 5x2 + 5x - 7; 0 and 1 50. ƒ1x2 = -2x3 + 9x2 - x - 20; 2 and 2.5 51. ƒ1x2 = 2x4 - 4x2 + 4x - 8; 1 and 2 52. ƒ1x2 = x4 - 4x3 - x + 3; 0.5 and 1 53. ƒ1x2 = x4 + x3 - 6x2 - 20x - 16; 3.2 and 3.3 54. ƒ1x2 = x4 - 2x3 - 2x2 - 18x + 5; 3.7 and 3.8 55. ƒ1x2 = x4 - 4x3 - 20x2 + 32x + 12; -1 and 0 56. ƒ1x2 = x5 + 2x4 + x3 + 3; -1.8 and -1.7 Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6. 57. ƒ1x2 = x4 - x3 + 3x2 - 8x + 8; no real zero greater than 2 58. ƒ1x2 = 2x5 - x4 + 2x3 - 2x2 + 4x - 4; no real zero greater than 1 59. ƒ1x2 = x4 + x3 - x2 + 3; no real zero less than -2
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