438 CHAPTER 6 Trigonometric Functions (e) For what numbers x, π π − ≤ ≤ x 2 2 , does ( ) = g x 1? Where does ( ) = − g x 1? (f) For what numbers x, π π − ≤ ≤ x 2 2 , does ( ) = g x 3 2 ? (g) What are the x-intercepts of g? 14. ( ) = g x x cos (a) What is the y-intercept of the graph of g? (b) For what numbers x, π π − ≤ ≤ x , is the graph of g decreasing? (c) What is the absolute minimum of g? (d) For what numbers x, π ≤ ≤ x 0 2 , does ( ) = g x 0? In Problems 15–24, determine the amplitude and period of each function without graphing. 15. = y x 5sin 16. = y x 3cos 17. ( ) = − y x 3cos 4 18. ( ) = − y x sin 1 2 19. π( ) = y x 6 sin 20. ( ) = − y x 3cos 3 21. ( ) = − y x 1 7 cos 7 2 22. ( ) = y x 4 3 sin 2 3 23. π ( ) = − y x 10 9 sin 2 5 24. π ( ) = − y x 9 5 cos 3 2 In Problems 25–34, match the given function to one of the graphs (A)–(J). 25. π( ) = y x 2 sin 2 26. π( ) = y x 2 cos 2 27. ( ) = y x 2cos 1 2 28. ( ) = y x 3cos 2 29. ( ) = − y x 3sin 2 30. ( ) = y x 2 sin 1 2 31. ( ) = − y x 2cos 1 2 32. π( ) = − y x 2cos 2 33. ( ) = y x 3sin 2 34. ( ) = − y x 2 sin 1 2 x y 2 22 22p 2p 4p (B) x y 2 22 22p 2p 4p (C) x y 2 22 (D) 22p 3 p p 2p 5p x y 2 22 22 2 21 1 3 4 5 (E) x y 2 22 22 2 21 1 3 4 5 (F) x y 2 22 22 2 4 (G) x y 3 23 (I) p p – 2 p – 2 2 x y 3 23 (H) p p – 2 3p ––– 4 5p ––– 4 2 p – 4 p – 4 p –– 2 2 x y 3 23 (J) 3p ––– 4 5p ––– 4 p – 4 p – 4 2 In Problems 35–58, graph each function using transformations or the method of key points. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. 35. = y x 4cos 36. = y x 3sin 37. = − y x 4 sin 38. = − y x 3cos 39. ( ) = y x cos 4 40. ( ) = y x sin 3 41. ( ) = − y x sin 2 42. ( ) = − y x cos 2 x y 2 22 22p 2p 4p (A)
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