289 2.7 Graphing Techniques (c) The graph of k1x2 = ƒ1x - 22 + 3 will look like the graph of ƒ1x2 translated to the right 2 units and up 3 units, as shown in Figure 91(c). (d) The graph of F1x2 = -ƒ1x2 is that of y = ƒ1x2 reflected across the x-axis. See Figure 91(d). S Now Try Exercise 93. –4 3 0 –4 2 x y y = f(x) Figure 90 EXAMPLE 9 GraphingTranslations and Reflections of a Given Graph A graph of a function y = ƒ1x2 is shown in Figure 90. Use this graph to sketch each of the following graphs. (a) g1x2 = ƒ1x2 + 3 (b) h1x2 = ƒ1x + 32 (c) k1x2 = ƒ1x - 22 + 3 (d) F1x2 = - ƒ1x2 SOLUTION In each part, pay close attention to how the plotted points in Figure 90 are translated or reflected. (a) The graph of g1x2 = ƒ1x2 + 3 is the same as the graph in Figure 90, translated up 3 units. See Figure 91(a). (b) To obtain the graph of h1x2 = ƒ1x + 32, the graph of y = ƒ1x2 must be translated to the left 3 units because x + 3 = 0 when x = -3. See Figure 91(b). h(x) = f(x + 3) –7 –3 –4 3 0 x y (b) –4 –2 3 x y g(x) = f(x) + 3 3 0 5 –1 3 0 x y k(x) = f(x – 2) + 3 (c) 5 –2 4 3 –4 0 x y F(x) = –f(x) (d) Figure 91 (a)
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