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3.4 Altered Functions, Altered Graphs: Stretching, Shrinking, Shifting, and Flipping 131 y y x f(x) = x2 –1 1 x –1 f(x) = x2 –1 y y x x y = 1 –1 y = x2 –1 x = –1 x = 1 Figure 3.13 Answers to Selected Exercises Answer to Exercise 3.7 undened for 0 for 0 h 1 x Figure 3.14 Your calculator probably won’t indicate the pinhole in the graph. Answer to Exercise 3.8 i. 3 3 1 23 3 6 7.5 132 CHAPTER 3 Functions Working Together ii. 1 11 2 1 1 2 2 1 1 2 2 2 3 1 iii. 1 11 21 1 1 1 2 1 2 1 1 2 1 If you want to add the fractions, get a common denominator. 21 2 2 2 1 1 1 1 iv. 2 2 1 1 1 1 22 22 2 22 2 1 22 4 22 1 v. 2 21 22 21 4 2 421 21 21 2824 21 3.4 Altered Functions, Altered Graphs: Stretching, Shrinking, Shifting, and Flipping 133 82 21 21 821 21 82 241 21 21 Solution to Exercise 3.11 All but the last two pairs of functions give a decomposition. P R O B L E M S F O R S E C T I O N 3 . 4 1. The zeros of the function are at 4, 1, 2, and 8. What are the zeros of (a) (5? (b) 2? (c) 2? (d) 1? Verify your answers analytically. 2. The zeros of the function are at 5, 2, 0, and 5. Find the zeros of the following functions. If there is not enough information to determine this, say so. (a) 3 (b) #, where #22 (c) 31 (d) 4 1 (e) (4 (f) $ 3. Thegraphof issymmetricaboutthe -axis.Whichofthefollowingfunctions is equal to ? (a) (b) (c) 4. Usingwhatyouknowaboutshifting,ipping,andstretching,matchthegraphsonpage 135 with the equations. (a) (b) (c) (d) (e) 3 1 3 1 1 2 1 1 2 1 134 CHAPTER 3 Functions Working Together y y y (i) (ii) (iii) y = 2 x x y = –1 x y y y (iv) (v) (vi) x 5. Below is the graph of 2. x y = –1 x As , . As , 0. y 2x 1 x Using what you know about shifting, ipping, and sliding, match the graphs on the following page with the equations. (a) 2 (b) 2 (c) 2 1 (d) 2 1 (e) 2 1 (f) 2 1 3.4 Altered Functions, Altered Graphs: Stretching, Shrinking, Shifting, and Flipping 135 y y y y (i) (ii) (iii) (iv) x x x x y y (v) (vi) y y (vii) (viii) x x x x 6. Using what you know about shifting, ipping, and stretching, match the graphs below with the equations. (a) 2 (b) 3 1 (c) 12 (d) 11 y y (i) (ii) y y (iii) (iv) x x x x y y (v) (vi) y y (vii) (viii) x x x yx 7. Applying what you learned in the last section of this chapter to the pocketful of functions you’ve been introduced to (the identity, squaring, reciprocal, and absolute value functions), graph the following functions. Label any asymptotes and - and -intercepts. ... - tailieumienphi.vn