Calculus Volume 1

58

Chapter 1 | Functions and Graphs

Figure 1.28 The function f ( x ) =− | x +2 | −3 can be viewed as a sequence of three transformations of the function y = | x |. b. Starting with the graph of y = x , reflect about the y -axis, stretch the graph vertically by a factor of 3, and move up 1 unit.

Figure 1.29 The function f ( x ) =3 − x +1 can be viewed as a sequence of three transformations of the function y = x .

1.16 Describe how the function f ( x ) =−( x +1) 2 −4 can be graphed using the graph of y = x 2 and a sequence of transformations.

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