SECTION 1.3 Intercepts; Symmetry; Graphing Key Equations 27 In Problems 25–34, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis; (b) the y-axis; (c) the origin. 25. ( ) 3, 4 26. ( ) 5, 3 27. ( ) −2, 1 28. ( ) − 4, 2 29. ( ) − 5, 2 30. ( ) − − 1, 1 31. ( ) − − 3, 4 32. ( ) 4, 0 33. ( ) − 0, 3 34. ( ) −3, 0 In Problems 35–46, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, the origin or none of these. 35. 3 –3 x y 3 –3 36. 3 23 x y 3 23 37. x y p 1 21 2p p–– 2 2 p–– 2 38. x y 3 4 24 23 39. x y 3 3 –3 –3 40. x y 3 3 –3 –3 41. y 6 26 x 3 23 42. 40 240 x 6 26 y 43. y 3 23 x 3 23 44. y 3 23 x 3 23 45. 22 28 8 2 46. 24 24 4 4 In Problems 47–50, draw a complete graph so that it has the type of symmetry indicated. 47. y-axis 9 –9 –9 9 x y (0, –9) (2, –5) 48. x-axis x y –5 5 –5 5 (–4, 0) (0, 2) (5, 3) 49. Origin x y –4 4 p–– 2 (p, 0) (0, 0) ( , 2) 50. y-axis y –3 3 –2 4 (0, 4) (0, 0) (2, 2) x In Problems 51–66, list the intercepts and test for symmetry. 51. = + y x 16 2 52. = + y x 9 2 53. = y x 3 54. = y x 5 55. + − = x y 9 0 2 56. − − = x y 4 0 2 57. + = x y 25 4 100 2 2 58. + = x y 4 4 2 2 59. = − y x 64 3 60. = − y x 1 4 61. = − − y x x2 8 2 62. = + y x 4 2 63. = + y x x 4 16 2 64. = − y x x 4 2 2 65. = − − y x x 9 3 2 66. = + y x x 1 2 4 5 In Problems 67–70, graph each equation. 67. = y x3 68. = x y2 69. = y x 70. = y x 1 71. If ( ) a, 4 is a point on the graph of = + y x x3 , 2 what is a? 72. If ( ) − a, 5 is a point on the graph of = + y x x6 , 2 what is a? Mixed Practice In Problems 73–80, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility. 73. = − y x 5 2 74. = − y x 8 2 75. − = − x y 9 2 76. + = x y 4 2 77. + = x y 9 2 2 78. + = x y 16 2 2 79. = − y x x4 3 80. = − y x x 3
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