AN2 Answers: Chapter 1 1.3 Assess Your Understanding (page 26) 3. intercepts 4. = y 0 5. y-axis 6. 4 7. ( ) −3, 4 8. T 9. F 10. F 11. d 12. c 13. ( ) −2, 0 , ( ) 0, 2 y 5 x 5 ( 2, 0) (0, 2) y x 2 15. ( ) −4, 0 , ( ) 0, 8 y 10 x 10 ( 4, 0) (0, 8) y 2x 8 17. ( ) ( ) ( ) − − 1,0, 1,0, 0, 1 y 5 x 5 ( 1, 0) (0, 1) (1, 0) y x2 1 19. ( ) ( ) ( ) −2, 0 , 2, 0 , 0, 4 y 5 x 5 ( 2, 0) (0, 4) (2, 0) y x2 4 21. ( ) 3, 0 , ( ) 0, 2 y 5 x 5 (0, 2) (3, 0) 2x 3y 6 33. y 5 x 5 (b) (0, 3) (a) (0, 3) (c) (0, 3) (0, 3) 23. ( ) −2, 0 , ( ) 2, 0 , ( ) 0, 9 y 10 x 10 ( 2, 0) (0, 9) (2, 0) 9x2 4y 36 25. y 5 x 5 (b) ( 3, 4) (a) (3, 4) (c) (3, 4) (3, 4) 27. y 5 x 5 (b) (2, 1) (c) (2, 1) (a) (2, 1) ( 2, 1) 29. y 5 x 5 (c) ( 5, 2) (b) (5, 2) (a) (5, 2) (5, 2) 31. y 5 x 5 (a) ( 3, 4) (b) (3, 4) (c) (3, 4) (3, 4) 35. (a) ( ) −1, 0 , ( ) 1, 0 (b) Symmetric with respect to the x-axis, the y-axis, and the origin 37. (a) π π ( ) ( ) ( ) − 2 ,0 , 0,1 , 2 , 0 (b) Symmetric with respect to the y-axis 39. (a) ( ) 0, 0 (b) Symmetric with respect to the x-axis 41. (a) ( ) −2, 0 , ( ) 0, 0 , ( ) 2, 0 (b) Symmetric with respect to the origin 43. (a) ( ) − ≤ ≤ x x , 0 , 2 1 (b) No symmetry 45. (a) No intercepts (b) Symmetric with respect to the origin 47. y 4 x 5 (2, 5) (0, 9) (2, 5) 49. y 5 x 5 ( , 0) ( , 0) 2 , 2 2 , 2 (0, 0) 51. ( ) ( ) ( ) − − 16, 0 , 0, 4 , 0, 4 ; symmetric with respect to the x-axis 53. ( ) 0, 0 ; symmetric with respect to the origin 55. ( ) ( ) ( ) − 0,9, 3,0, 3, 0 ; symmetric with respect to the y-axis 57. ( ) ( ) ( ) − − 2,0, 2,0, 0, 5, ( ) 0, 5 ; symmetric with respect to the x-axis, the y-axis, and the origin 59. ( ) − 0, 64, ( ) 4, 0 ; no symmetry 61. ( ) − 0, 8, ( ) 4, 0 , ( ) −2, 0 ; no symmetry 63. ( ) 0, 0 ; symmetric with respect to the origin 65. ( ) 0, 0 ; symmetric with respect to the origin 67. y 5 x 5 (0, 0) (1, 1) (1, 1) 69. y 5 x 5 (4, 2) (1, 1) (0, 0) 71. = − = a a 4 or 1 73. (a) ( ) ( ) ( ) − − 0, 5, 5, 0 , 5, 0 (b) Symmetric with respect to the y-axis 81. ( ) − − 1, 2 83. 4 85. (a) ( ) 0, 0 , ( ) 2, 0 , ( ) 0, 1 , ( ) − 0, 1 (b) x-axis symmetry 87. ( ) ( ) −a 0, 0 , , 0 , ( ) a, 0 ; symmetric with respect to the x-axis, the y-axis, and the origin 1.5 Assess Your Understanding (page 43) 1. (a) = = = Rise 2; Run 2; Slope 1 (b) = − Slope 2 (c) = Slope 0 (d) ii and iv (e) ii 2. undefined; 0 3. 3; 2 4. T 5. F 6. T 7. = m m ; 1 2 y-intercepts; = − mm 1 1 2 8. 2 9. − 1 2 10. d 11. b 12. d (c) y 2 x 5 (2, 21) (1, 24) (21, 24) (22, 21) (0, 25) (2 5, 0) ( 5, 0) y 5 x2 2 5 75. (a) ( ) ( ) ( ) − − 9,0, 0, 3, 0,3 (b) Symmetric with respect to the x-axis (c) y 5 x 1 (0, 23) (0, 3) (29, 0) or y 5 1 2 x 1 9 x 2 y2 5 29 77. (a) ( ) ( ) ( ) ( ) − − 0,3,0, 3, 3,0, 3,0 (b) Symmetric with respect to the x-axis, y-axis, and origin (c) y 5 x 5 (0, 3) (3, 0) (0, 23) (23, 0) x2 1 y2 5 9 Circle, radius 3 79. (a) ( ) ( ) ( ) − 0, 0 , 2, 0 , 2, 0 (b) Symmetric with respect to the origin (c) y 5 x 5 (2, 0) (1, 23) (22, 0) (21, 3) y 5 x3 2 4x 69. Arrange the parallelogram on the coordinate plane so that the vertices are ( ) ( ) ( ) = = = + P P a P a b c 0, 0 , , 0 , , 1 2 3 and ( ) = P b c , 4 . Then the lengths of the sides are ( ) ( ) ( ) = = + = dPP adPP b c dPP a , , , , , 1 2 2 3 2 2 3 4 , and ( ) = + d P P b c , 1 4 2 2 , and the lengths of the diagonals are ( ) ( ) = + + d P P a b c , 1 3 2 2 and ( ) ( ) = − + d P P a b c , 2 4 2 2 . So, the sum of the squares of the lengths of the sides is ( ) ( ) + + ++ + =+++++= + + a b c a b c a b c a b c a b c 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2.The sum of the squares of the lengths of the diagonals is ( ) ( ) ( ) ( ) ( ) ( ) ++ + −+ =+++−+=++++−++= ++ a b c a b c a b c a b c a ab b c a ab b c a b c 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2. 1.4 Assess Your Understanding (page 31) 3. ZERO (or ROOT) 4. F 5. { } −2.21, 0.54, 1.68 7. { } −1.55, 1.15 9. { } −1.12, 0.36 11. { } − − 2.69, 0.49, 1.51 13. { } − − 2.86, 1.34, 0.20, 1.00 15. No real solutions 17. { } −18 19. { } −4 21. { } 46 5 23. { }3 25. { }2 27. { } −4, 7 29. { } − 2 3 , 2 31. { } − − 2, 1, 2 33. { } 15 35. { } − − 4, 1 8
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