293 2.7 Graphing Techniques Concept Check Suppose the point 18, 122 is on the graph of y = ƒ1x2. 35. Find a point on the graph of (a) y = ƒ1x + 42 (b) y = ƒ1x2 + 4. 36. Find a point on the graph of (a) y = 1 4 ƒ1x2 (b) y = 4ƒ1x2. 37. Find a point on the graph of (a) y = ƒ14x2 (b) y = ƒ A1 4 xB. 38. Find a point on the graph of the reflection of y = ƒ1x2 (a) across the x-axis (b) across the y-axis. Concept Check Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin. 39. 15, -32 40. 1-6, 12 41. 1-4, -22 42. 1-8, 02 43. Concept Check The graph of y = 0 x - 20 is symmetric with respect to a vertical line. What is the equation of that line? 44. Concept Check Repeat Exercise 43 for the graph of y = -0 x + 10 . Without graphing, determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. See Examples 3 and 4. 45. y = x2 + 5 46. y = 2x4 - 3 47. x2 + y2 = 12 48. y2 - x2 = -6 49. y = -4x3 + x 50. y = x3 - x 51. y = x2 - x + 8 52. y = x + 15 53. x = y 54. x2 = - y 55. 1 x2 + 1 2y = 25 56. 2 y2 + 3 x = 4 Determine whether each function is even, odd, or neither. See Example 5. 57. ƒ1x2 = -x3 + 2x 58. ƒ1x2 = x5 - 2x3 59. ƒ1x2 = 0.5x4 - 2x2 + 6 60. ƒ1x2 = 0.75x2 + 0 x 0 + 4 61. ƒ1x2 = x3 - x + 9 62. ƒ1x2 = x4 - 5x + 8 63. ƒ1x2 = x + 1 x5 64. ƒ1x2 = x4 + 4 x2 Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. 65. ƒ1x2 = x2 - 1 66. ƒ1x2 = x2 - 2 67. ƒ1x2 = x2 + 2 68. ƒ1x2 = x2 + 3 69. g1x2 = 1x - 422 70. g1x2 = 1x - 222 71. g1x2 = 1x + 222 72. g1x2 = 1x + 322 73. g1x2 = 0 x 0 - 1 74. g1x2 = 0 x + 30 + 2 75. h1x2 = -1x + 123 76. h1x2 = -1x - 123 77. h1x2 = 2x2 - 1 78. h1x2 = 3x2 - 2 79. ƒ1x2 = 21x - 222 - 4 29. h1x2 = ` - 1 2 x ` 30. h1x2 = ` - 1 3 x ` 31. h1x2 = 24x 32. h1x2 = 29x 33. ƒ1x2 = -2-x 34. ƒ1x2 = -0 -x 0
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