chapter 1 38 - 38 CHAPTER 1 FUNCTIONS AND MODELS 9 We start...

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Unformatted text preview: 38 CHAPTER 1 FUNCTIONS AND MODELS 9. We start with the graph of y = 23” y (Figure 2). reflect it about the y—axis. and then about the ac—axis —i) x (or just rotate 1800 to handle both reflections) to obtain the graph of y : —2_“”. In each graph. y = 0 is the horizontal asymptote. I y = 2 y = —2‘“” 10. We start with the graph of y : ex (Figure 13). 11. We start with the graph ofy : 6“ (Figure 13), vertically stretch by a factor of 2. and then shift reflect it about the m—axis, and then shift 3 units 1 unit upward. There is a horizontal asymptote upward. Note the horizontal asymptote of y : 3. of y : 1. _v 2 0 3 y : 26$ y : 1 + 261: 12. We start with the graph of y = e“E (Figure 13), reflect it about the y—axis. and then about the as-axis (or just rotate 180° to handle both reflections) to obtain the graph of y 2 76’“. Now shift this graph 1 unit upward. vertically stretch by a factor of 5, and then shift 2 units upward. y:2+5(1—e—m) 13. (a) To find the equation of the graph that results from shifting the graph of y : e“6 2 units downward, we subtract 2 from the original function to get y : e$ i 2. (b) To find the equation of the graph that results from shifting the graph of y : em 2 units to the right, we replace m with m — 2 in the original function to get y : 6(172). (c) To find the equation of the graph that results from reflecting the graph of y : 61 about the x—axis. we multiply the original function by 71 to get y : —e“”. (d) To find the equation of the graph that results from reflecting the graph of y : er” about the y—axis, we replace a: with 7:1: in the original function to get y : e". (e) To find the equation of the graph that results from reflecting the graph of y : e“ about the ac—axis and then about the y—axis. we first multiply the original function by 71 (to get y = —e’) and then replace m with em in this equation to get y : #e ...
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