SECTION A.1 Algebra Essentials A11 Skill Building In Problems 11–22, use U = universal set A B 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 , 1, 3, 4, 5, 9 , 2, 4, 6, 7, 8 , { } { } { } = = = and C 1, 3, 4, 6 { } = to find each set. 11. A B ∪ 12. A C∪ 13. A B ∩ 14. A C∩ 15. A B C ( ) ∪ ∩ 16. A B C ( ) ∩ ∪ 17. A 18. C 19. A B ∩ 20. B C∪ 21. A B ∪ 22. B C∩ 23. On the real number line, label the points with coordinates 0, 1, 1, 5 2 , 2.5, 3 4 , − − and 0.25. 24. Repeat Problem 23 for the coordinates 0, 2, 2, 1.5, 3 2 , 1 3 , − − and 2 3 . In Problems 25–34, replace the question mark by , , < > or ,= whichever is correct. 25. 1 2 ? 0 26. 5 ? 6 27. 1 ? 2 − − 28. 3 ? 5 2 − − 29. ? 3.14 π 30. 2 ? 1.41 31. 1 2 ? 0.5 32. 1 3 ? 0.33 33. 2 3 ? 0.67 34. 1 4 ? 0.25 In Problems 35–40, write each statement as an inequality. 35. x is positive 36. z is negative 37. x is less than 2 38. y is greater than 5− 39. x is less than or equal to 1 40. x is greater than or equal to 2 In Problems 41–44, graph the numbers x on the real number line. 41. x 2 ≥− 42. x 4 < 43. x 1 >− 44. x 7 ≤ In Problems 45–50, use the given real number line to compute each distance. A B C D E 0 1 2 3 4 5 6 -1 -2 -3 -4 45. d C D , ( ) 46. d C A , ( ) 47. d D E , ( ) 48. d C E , ( ) 49. d A E , ( ) 50. d D B , ( ) In Problems 51–58, evaluate each expression if x 2 = − and y 3. = 51. x y2 + 52. x y 3 + 53. xy 5 2 + 54. x xy 2− + 55. x x y 2 − 56. x y x y + − 57. x y y 3 2 2 + + 58. x y 2 3 − In Problems 59–68, find the value of each expression if x 3 = and y 2. = − 59. x y + 60. x y − 61. x y + 62. x y − 63. x x 64. y y 65. x y 4 5 − 66. x y 3 2 + 67. x y 4 5 − 68. x y 3 2 + In Problems 69–76, determine which of the values (a) through (d), if any, must be excluded from the domain of the variable in each expression. (a) x 3 = (b) x 1 = (c) x 0 = (d) x 1 = − 69. x x 1 2 − 70. x x 1 2 + 71. x x 9 2 − 72. x x 9 2 + 73. x x 1 2 2 + 74. x x 1 3 2 − 75. x x x x 5 10 2 3 + − − 76. x x x x 9 1 2 3 − − + + In Problems 77–80, determine the domain of the variable x in each expression. 77. x 4 5 − 78. x 6 4 − + 79. x x 4 + 80. x x 2 6 − −
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