640 CHAPTER 6 The Circular Functions and Their Graphs Concept Check Match each function with its graph in choices A – I. (One choice will not be used.) 9. y = sin ax - p 4b 10. y = sin ax + p 4b 11. y = cos ax - p 4b 12. y = cos ax + p 4b 13. y = 1 + sin x 14. y = -1 + sin x 15. y = 1 + cos x 16. y = -1 + cos x A. y 0 1 –1 x – 7p 4 3p 4 p 4 D. x y –1 0 1 9p 4 5p 4 p 4 G. y 0 1 –1 x – 7p 4 3p 4 p 4 B. x y 0 –1 1 2 2 p p E. x y 0 –1 –2 1 2p p H. y x 0 –1 1 9p 4 5p 4 p 4 C. x y –2 0 –1 1 2p p F. x y 0 1 2 2p p I. x y 0 –1 1 2 2p p 3. The graph of y = 4 sin x is obtained by stretching the graph of y = sin x vertically by a factor of . 4. The graph of y = -3 sin x is obtained by stretching the graph of y = sin x by a factor of and reflecting across the -axis. 5. The graph of y = 6 + 3 sin x is obtained by shifting the graph of y = 3 sin x unit(s) . (up / down) 6. The graph of y = -5 + 2 cos x is obtained by shifting the graph of y = 2 cos x unit(s) . (up / down) 7. The graph of y = 3 + 5 cos Ax + p 5 B is obtained by shifting the graph of y = cos x horizontally unit(s) to the , stretching it vertically by a factor of , and then shifting it vertically unit(s) . (up / down) 8. The graph of y = -2 + 3 cos Ax - p 6 B is obtained by shifting the graph of y = cos x horizontally unit(s) to the , stretching it vertically by a factor of , and then shifting it vertically unit(s) . (up / down) (right / left) (right / left) 17. The graphs of y = sin x + 1 and y = sin1x + 12 are NOT the same. Explain why this is so.
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