Exam (elaborations) TEST BANK FOR Calculus 8th Editon (3 Volume Set) By Ron Larson, Robert P. Hostetler and Bruce H. Edwards (Study And Solutions Guide)

Section P.1 Graphs and Models Solutions to Odd-Numbered Exercises 2 1. x-intercept: y-intercept: Matches graph (b) 0, 2 4, 0 y  12 x  2 3. x-intercepts: y-intercept: Matches graph (a) 0, 4 2, 0, 2, 0 y  4  x2 5. x 2 2 −4 −6 −8 4 6 8 −8 −6 −4 4 6 8 (−4, −5) (−2, −2) (0, 1) (2, 4) (4, 7) y y  32 x  1 7. x 2 −4 −2 −6 6 −6 −4 4 6 (−3, −5) (3, −5) (−2, 0) (0, 4) (2, 0) y y  4  x2 x 0 2 4 y 5 2 1 4 7 4 2 x 0 2 3 y 5 0 4 0 5 3 2 9. x 2 −2 4 6 −6 −4 2 (−3, 1) (−1, 1) (−4, 2) (−2, 0) (0, 2) (1, 3) (−5, 3) y y  x  2 11. x 4 6 8 2 −6 −8 −4 −10 10 − 18 (0, −4) (1, −3) (4, −2) (16, 0) y (9, −1) y  x  4 x 0 1 y 3 2 1 0 1 2 3 5 4 3 2 1 x 0 1 4 9 16 y 4 3 2 1 0 Section P.1 Graphs and Models 3 13. Note that y  4 when x  0. Xmin = -3 Xmax = 5 Xscl = 1 Ymin = -3 Ymax = 5 Yscl = 1 15. (a) (b) x, 3  4, 3 3  5  4 2, y  2, 1.73 y  5  2  3  1.73 −6 6 −3 5 (−4.00, 3) (2, 1.73) 17. y-intercept: x-intercepts: x  2, 1; 2, 0, 1, 0 0  x  2x  1 0  x2  x  2 y  2; 0, 2 y  02  0  2 y  x2  x  2 19. y-intercept: x-intercepts: x  0, ±5; 0, 0; ±5, 0 0  x25  x5  x 0  x225  x2 y  0; 0, 0 y  0225  02 y  x225  x2 21. y-intercept: None. x cannot equal 0. x-intercepts: x  4; 4, 0 0  2  x 0  32  x x y  32  x x 23. y-intercept: x-intercept: x  0; 0, 0 x20  x2  40  0 y  0; 0, 0 02y  02  4y  0 x2y  x2  4y  0 25. Symmetric with respect to the y-axis since y  x2  2  x2  2. 27. Symmetric with respect to the x-axis since y2  y2  x3  4x. 29. Symmetric with respect to the origin since xy  xy  4. 31. No symmetry with respect to either axis or the origin. y  4  x  3 33. Symmetric with respect to the origin since y  x x2  1 . y  x x2  1 35. is symmetric with respect to the y-axis since y  x3  x  x3  x  x3  x. y  x3  x 37. Intercepts: Symmetry: none 23 , 0, 0, 2 0 y 2 (0, 2) 1 x 1 2 3 1 , 23 y  3x  2 4 Chapter P Preparation for Calculus 39. Intercepts: Symmetry: none x 8 10 (8, 0) y 2 4 , 4) 2 ( 2 0 2 8 6 10 8, 0, 0, 4 y  x 2  4 41. Intercepts: Symmetry: y-axis x (1, 0) 0, 1) y 2 ( 1, 0) ( 1 2 −2 2 1, 0, 1, 0, 0, 1 y  1  x2 43. Intercepts: Symmetry: none x 2 −2 8 10 12 −10 −8 −6 (−3, 0) 2 4 (0, 9) y 3, 0, 0, 9 y  x  32 45. Intercepts: Symmetry: none y 5 4 3 3 x 2 3 , 1 1 1 , 3 2 ( 2 0) (0 2) 3 2, 0, 0, 2 y  x3  2 47. Intercepts: Symmetry: none Domain: x 1 2 3 4 5 −2 6 −4 −3 −1 1 2 3 4 (−2, 0) (0, 0) y x ≥ 2 0, 0, 2, 0 y  xx  2 49. Intercepts: Symmetry: origin x 1 −2 −3 −4 2 3 4 −4 −3 −2 −1 2 3 4 (0, 0) y 0, 0 x  y3 51. Intercepts: none Symmetry: origin y 3 1 2 x 1 2 3 y  1 x 53. Intercepts: Symmetry: y-axis 0, 6, 6, 0, 6, 0 x 2 2 −4 −2 −6 −8 4 6 8 −8 −4 −2 4 6 8 (−6, 0) (0, 6) (6, 0) y  6  x y 55. Intercepts: Symmetry: x-axis 0, 3, 0, 3, 9, 0 1 −4 −11 4 (−9, 0) (0, −3) (0, 3) y  ±x  9 y2  x  9 y2  x  9 57. Intercepts: Symmetry: x-axis 6, 0, 0, 2, 0, 2 8 −3 −1 3 (6, 0) (0 , 2 ) ( 0 , − 2 ) y  ±2  x 3 3y2  6  x x  3y2  6 Section P.1 Graphs and Models 5 59. y  x  2x  4x  6 (other answers possible) 61. Some possible equations: y  3 x y  3x3  x y  x3 y  x 63. The corresponding y-value is Point of intersection: 1, 1 y  1. 1  x 3  3x 2  x  2x  1 2x  y  1 ⇒y  2x  1 x  y  2 ⇒y  2  x 65. The corresponding y-value is Point of intersection: 5, 2 y  2. x  5 5x  25 14  2x  3x  11 7  x  3x  11 2 3x  2y  11 ⇒y  3x  11 2 x  y  7 ⇒y  7  x 67. The corresponding y-values are (for ) and (for ). Points of intersection: 2, 2, 1, 5 y  5 x  1 y  2 x  2 x  2, 1 0  x  2x  1 0  x2  x  2 6  x2  4  x x  y  4 ⇒y  4  x x2  y  6 ⇒y  6  x2 69. The corresponding y-values are and Points of intersection: 1, 2, 2, 1 y  2 y  1. x  1 or x  2 0  2x2  2x  4  2x  1x  2 5  x2  x2  2x  1 5  x2  x  12 x  y  1 ⇒y  x  1 x2  y2  5 ⇒y2  5  x2 71. The corresponding y-values are and Points of intersection: 0, 0, 1, 1, 1, 1 y  1. y  0, y  1, x  0, x  1, or x  1 xx  1x  1  0 x3  x  0 x3  x y  x y  x3 73. −4 6 −8 4 y = −x 2 + 3x − 1 y = x 3 − 2x 2 + x − 1 (2, 1) (0, −1) (− 1 , −5) 1, 5, 0, 1, 2, 1 x  1, 0, 2