chapter 1 18 - 18 CHAPTER 1 FUNCTIONS AND MODELS 5(a To...

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Unformatted text preview: 18 CHAPTER 1 FUNCTIONS AND MODELS 5. (a) To graph y = f (23c) we shrink the graph of f (b) To graph y = f (ém) we stretch the graph of f horizontally by a factor of 2. horizontally by a factor of 2. The point (47 —1) on the graph of f corresponds ' tothe oint 2-4,—1 = 87—1, The p01nt (4, —1) on the graph of f corresponds p ( ) ( ) to the point (i -4, —1) : (27 —1). (c) To graph y : f (—511) we reflect the graph of f (d) To graph y = — f (—x) we reflect the graph of f about the y—axis. about the y-axis, then about the x—axis. The point (4, #1) on the graph of f corresponds to the point (_1 _ 47 _1) = (_4, _1). The point (4, —1) on the graph of f corresponds to the point (—1 - 47 —1 - —1) = (—4, 1). 6. The graph of y = f (0:) = \/ 31: — $2 has been shifted 2 units to the right and stretched vertically by a factor of 2. Thus, a function describing the graph is y:2f(m—2)=2V3(:E—2)—(m——2)2 :2x/3m—6-(w2—4$+4)=2 —$2+7m—10 7. The graph of y = f (as) = \/ 3m — x2 has been shifted 4 units to the left, reflected about the :c—axis, and shifted downward 1 unit. Thus, a function describing the graph is y: —1- f(w+4) —1 v WV reflect shift shift about 4 units 1 unit ac—axis left down This function can be written as y=#f(x+4)—1:# 3(m+4)—($+4)2—1=—\/32:+12—(ac2+8m+16)—1 :7 ~w2—5w—4—1 ...
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