319 CHAPTER 2 Review Exercises Graph each function. 69. ƒ1x2 = 0 x 0 - 3 70. ƒ1x2 = -0 x 0 71. ƒ1x2 = -1x + 122 + 3 72. ƒ1x2 = -2x - 2 73. ƒ1x2 = Œx - 3œ 74. ƒ1x2 = 223 x + 1 - 2 75. ƒ1x2 = e -4x + 2 3x - 5 if x … 1 if x 71 76. ƒ1x2 = e x2 + 3 -x + 4 if x 62 if x Ú 2 77. ƒ1x2 = e 0 x 0 6 - x if x 63 if x Ú 3 78. Concept Check If x represents an integer, then what is the simplest form of the expression Œxœ + x? Concept Check Determine whether each statement is true or false. If false, tell why. 79. The graph of an even function is symmetric with respect to the y-axis. 80. The graph of a nonzero function cannot be symmetric with respect to the x-axis. 81. If 1a, b2 is on the graph of an even function, then so is 1a, -b2. 82. The graph of an odd function is symmetric with respect to the origin. 83. The constant function ƒ1x2 = 0 is both even and odd. 84. If 1a, b2 is on the graph of an odd function, then so is 1-a, b2. Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. 85. x + y2 = 10 86. 5y2 + 5x2 = 30 87. x2 = y3 88. y3 = x + 4 89. 6x + y = 4 90. 0 y 0 = -x 91. y = 1 92. 0 x 0 = 0 y 0 93. x2 - y2 = 0 94. x2 + 1y - 222 = 4 Describe how the graph of each function can be obtained from the graph of ƒ1x2 = 0 x 0 . 95. g1x2 = -0 x 0 96. h1x2 = 0 x 0 - 2 97. k1x2 = 20 x - 40 Let ƒ1x2 = 3x - 4. Find an equation for each reflection of the graph of ƒ1x2. 98. across the x-axis 99. across the y-axis 100. across the origin 101. Concept Check The graph of a function ƒ is shown in the figure. Sketch the graph of each function defined as follows. (a) y = ƒ1x2 + 3 (b) y = ƒ1x - 22 (c) y = ƒ1x + 32 - 2 (d) y = 0 ƒ1x2 0 102. Concept Check Must the domain of g be a subset of the domain of ƒ∘ g? Let ƒ1x2 = 3x2 - 4 and g1x2 = x2 - 3x - 4. Find each of the following. 103. 1ƒg21x2 104. 1ƒ - g2142 105. 1ƒ + g21-42 106. 1ƒ + g212k2 107. a ƒ gb132 108. a ƒ gb1-12 109. the domain of 1ƒg21x2 110. the domain of A f gB1x2 –4 4 8 –2 2 0 x y
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