(Every fourth, except for 79; pp.242-244)

ingles ek 2 - why are mar chapter 3 - Practice & assignment # 2 xamen 2 s signment # 2 draft. 242 CHAPTER 2 . Functions 2.6 EXERCISES 12. (a) y = f(x + 3) + 2 (b) y = f(x - 7) - 3 CONCEPTS 13. (a) y = -f(x) + 5 (b) y = 3f(x) - 5 1-2 = Fill in the blank with the appropriate direction (left, right, up, or down). 14. (a) 1 - f(-x) (b) 2 - 35(x ) 1. (a) The graph of y = f(x) + 3 is obtained from the graph 15. (a) 25 (x + 5 ) - 1 (b) 4f (x - 3) + 5 of y = f(x) by shifting - 3 units. 16. (a) 35(x - 2) + 5 ( b ) 4f ( x + 1 ) + 3 (b) The graph of y = f(x + 3) is obtained from the graph 17. (a) y = f(4x) (b) y = f(4x) of y = f(x) by shifting - 3 units. 18. (a) y = f(2x) - 1 (b) y = 2f(2x) 2. (a) The graph of y = f(x) - 3 is obtained from the graph 19-22 . Describing Transformations Explain how the graph of g of y = f(x) by shifting _ - 3 units. is obtained from the graph of f. (b) The graph of y = f(x - 3) is obtained from the graph 19. ( a ) f(x ) = x2 , 9 ( x ) = ( x + 2 ) 2 of y = f(x) by shifting 3 units. (b) f(x) = x2, 9(x) = x2+ 2 3. Fill in the blank with the appropriate axis (x-axis or y-axis). 20. (a) f (x) = x3, 9(x) = (x- 4)3 (a) The graph of y = -f(x) is obtained from the graph of ( b ) f ( x ) = x 3 , 9 (x ) = x3 - 4 y = f(x) by reflecting in the 21. (a) f (x) = 1x1, 9(x ) = 1x+21 - 2 (b) The graph of y = f(-x) is obtained from the graph of (b) f (x ) = 1x1, 9(x ) = 1x-21+ 2 y = f(x) by reflecting in the 22. (a) f ( x) = Vx, g(x) = - Vx+ 1 4. A graph of a function f is given. Match each equation with (b) f (x) = Vx, g(x) = V-x+ 1 one of the graphs labeled I-IV. (a) f(x) + 2 (b) f (x + 3) 23) Graphing Transformations Use the graph of y = x2 in Fig- (c) f(x - 2) (d) f(x) - 4 ure 4 to graph the following. (a) g(x) =x2+1 (b) g(x) = (x - 1)2 (c) g(x) = -x (d) g(x) = (x - 1)2+ 3 24. Graphing Transformations Use the graph of y = Vx in Fig- ure 5 to graph the following. (a) g(x) = Vx -2 (b) g(x) = Vx+1 c) g(x) = Vx+ 2+ 2 (d) g(x) = - Vx+1 25-28 - Identifying Transformations Match the graph with the function. (See the graph of y = | x | on page 202.) 25, y = |x+ 1 26. y = |x - 11 27. y = 1x1 -1 28. y = - 1x1 YA IT 5. If a function f is an even function, then what type of symme- try does the graph of f have? 6. If a function f is an odd function, then what type of symme- try does the graph of f have? TO 2 x 2 SKILLS 7-18 Describing Transformations Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f. III IV 7.) (a ) f( x ) - 1 (b) f(x - 2) 8. (a) f (x + 5 ) ( b) f ( x ) + 4 2+ 9. (a) f (-x ) ( 1) 3f (x ) 10. (a) - f(x) ( b ) 3f (x ) 2 11. (a ) y = f (x - 5 ) + 2 (b ) y = f (x+ 1 ) - 1 +SECTION 2.6 = Transformations of Functions 243 65. 66. 29-52 = Graphing Transformations Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. 29. f (x) = 12+3 30. f(x) - x2 - 4 (31 5 (x ) = 1x1 - 1 32. f (x) = Vx+ 1 -33. f (x) = (x - 5) 34. f(x) = (x + 1)2 67. 35 1 (x) = 1x+ 21 36. f(x) = Vx - 4 .37. f (x ) = -x 38. f(x) = -1x1 f ( x ) = Vx 69. Y = V-x 40. y = V-x (B) .41. y = 1x2 42. y = -5Vx (43 y = 31x1 44. = 21x/ 68. -45. y = (x - 3)2 + 5 46. y = Vx+ 4 -3 (47, y = 3 - 4(x - 1)2 48. y = 2 - Vx+ 1 f(x) = 12 49. y = 1x+ 21 + 2 50. y = 2-1x/ 51 y = V x + 4 -3 52. y =3-2(x - 1)3com 53-62 - Finding Equations for Transformations A function f is given, and the indicated transformations are applied to its graph 69-70 - Identifying Transformations The graph of y = f(x) is (in the given order). Write an equation for the final transformed given. Match each equation with its graph. graph 69. (a) y = f(x - 4) (b) y = f(x)+ 3 53. f(x) = x2; shift downward 3 units (c) y = 2f(x+ 6) (d) y = -f(2x) 54. f(x) = x'; shift upward 5 units 55. f(x) = Vx; shift 2 units to the left on 10 dibo nove el t nois YA 56. f(x) = Vx; shift 1 unit to the right ship Ageng all Hote 2 6 57. f(x) = |x|; shift 2 units to the left and shift downward 5 units 3 f ( x ) 3 58. f(x) = | x |; reflect in the x-axis, shift 4 units to the right, and shift upward 3 units. 59. f(x) = Vx; reflect in the y-axis and shift upward 1 unit 6 -3 60. f(x) = x2; shift 2 units to the left and reflect in the x-axis 61. f(x) = x2; stretch vertically by a factor of 2, shift downward 2 units, and shift 3 units to the right offonul () 62. f(x) = | x|; shrink vertically by a factor of 2, shift to the 70. (a) y = 3f(x) (b ) y = -f (x+ 4 ) left 1 unit, and shift upward 3 units (c) y = f(x - 4)+ 3 (d) y = f(-x) 63-68 - Finding Formulas for Transformations The graphs of f and g are given. Find a formula for the function g. 63. 64. f ( x) f(x) = 12 f ( x) = x3 beonfT nolfonut s to pulsV ofu -6 -3 0 mont boniado of | (O)t | = v 10 nge 6 x 3en 2 t Crafts 2.6 EXERCISES CONCEPTS 244 CHAPTER 2 . Functions 77-80 = Graphing Transformations Graph the functions on the 71-74 = Graphing Transformations The graph of a function f same screen using the given viewing rectangle. How is each graph is given. Sketch the graphs of the following transformations off related to the graph in part (a)? -71 (a) y = f(x - 2) ( b ) y = f ( x ) - 2 77. Viewing rectangle [ -8, 8 ] by [ -2. 8 ] (c) y = 2f(x) (d) y = -f(x) + 3 (a) y = Ve (b) y = Vx+ 5 (e) y = 1(-x) (ny = If(x - 1) (e) y = 2Vx + 5 (d) y = 4 + 2Vx + 5 78. Viewing rectangle [ -8, 8 ] by [-6. 6] (a) >= 1x/ (b ) y =- 1x1 c) y = -31x (d) y = -3/x-51 79 Viewing rectangle [ -4, 6] by [ -4, 4 ] a) y=.+6 (b) y = 4x6 (c) y= -1x (d) y = - 3(x - 4)6 80. Viewing rectangle [ -6, 6] by [-4, 4] (a) y = - (b) y = 72. (a) y = f(x + 1) (b) y = f ( -x) Vx Vx + 3 (c) y = f (x - 2) (d) y = f(x) - 2 (c) y = (e) y =-f(x) (n) y = 2f(x) 2 Vx+ 3 (d) y = 2 2Vx + 3 - 3 81-82 = Graphing Transformations If f(x) = V2x - x2, graph the following functions in the viewing rectangle [ -5, 5] by -4, 4]. How is each graph related to the graph in part (a)? 81. (a) y = f(x) (b) y = f(2x) (c ) y = f(2x) 82. (a) y = f(x) (b) y = f(-x) (c) y = -f(-x) (d) y = f(-2x) (e) y = f(-2x) 83-90 Even and Odd Functions Determine whether the func- 73. (a) y = f(2x) ( b ) y = f ( 2x ) tion f is even, odd, or neither. If f is even or odd, use symmetry to ketch its graph. ( 83) f ( x ) = x4 84. f (x ) = x3 * 85. f ( x ) = x2 + x 86. f(x) = x4 - 4x2 -87. f(x) = x3 - x 88. f(x) = 3x3 + 2x2 + 1 89. f (x) = 1 - Vx 90. f (x ) = x+_ x SKILLS Plus 74. (a) y = f(3x) (b) y = f(3x) 91-92 - Graphing Even and Odd Functions The graph of a function defined for x 2 0 is given. Complete the graph for x