429 63. Dimensions of a Box The width of a rectangular box is three times its height, and its length is 11 in. more than its height. Find the dimensions of the box if its volume is 720 in.3. 3x x x + 11 64. The function ƒ1x2 = 1 x is negative at x = -1 and positive at x = 1 but has no zero between -1 and 1. Explain why this does not contradict the intermediate value theorem. Graph each rational function. 65. ƒ1x2 = 4 x - 1 66. ƒ1x2 = 4x - 2 3x + 1 67. ƒ1x2 = 6x x2 + x - 2 68. ƒ1x2 = 2x x2 - 1 69. ƒ1x2 = x2 + 4 x + 2 70. ƒ1x2 = x2 - 1 x 71. ƒ1x2 = -2 x2 + 1 72. ƒ1x2 = 4x2 - 9 2x + 3 Solve each problem. 73. Concept Check Work each of the following. (a) Sketch the graph of a function that does not intersect its horizontal asymptote y = 1, has the line x = 3 as a vertical asymptote, and has x-intercepts 12, 02 and 14, 02. (b) Find an equation for a possible corresponding rational function. 74. Concept Check Work each of the following. (a) Sketch the graph of a function that is never negative and has the lines x = -1 and x = 1 as vertical asymptotes, the x-axis as a horizontal asymptote, and the origin as an x-intercept. (b) Find an equation for a possible corresponding rational function. 75. Connecting Graphs with Equations Find a rational function ƒ having the graph shown. x y 0 –3 –6 1 2 x = 1 y = –3 CHAPTER 3 Review Exercises 62. Dimensions of a Cube After a 2-in. slice is cut off the top of a cube, the resulting solid has a volume of 32 in.3. Find the dimensions of the original cube. 2 x x x – 2
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