295 2.7 Graphing Techniques Concept Check Suppose that for a function ƒ, ƒ132 = 6. For the given assumptions, find another function value. 101. The graph of y = ƒ1x2 is symmetric with respect to the origin. 102. The graph of y = ƒ1x2 is symmetric with respect to the y-axis. 103. The graph of y = ƒ1x2 is symmetric with respect to the line x = 6. 104. For all x, ƒ1-x2 = ƒ1x2. 105. For all x, ƒ1-x2 = -ƒ1x2. 106. ƒ is an odd function. Work each problem. 107. Find a function g1x2 = ax + b whose graph can be obtained by translating the graph of ƒ1x2 = 2x + 5 up 2 units and to the left 3 units. 108. Find a function g1x2 = ax + b whose graph can be obtained by translating the graph of ƒ1x2 = 3 - x down 2 units and to the right 3 units. 109. Concept Check Complete the left half of the graph of y = ƒ1x2 in the figure for each condition. (a) ƒ1-x2 = ƒ1x2 (b) ƒ1-x2 = -ƒ1x2 x y 2 2 0 y = f(x) 110. Concept Check Complete the right half of the graph of y = ƒ1x2 in the figure for each condition. (a) ƒ is odd. (b) ƒ is even. 99. x y 5 2 0 100. –2 –4 y –2 0 2 x x y 2 –2 0 y = f(x)
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