A-21 Answers to Selected Exercises 81. x y 1 2 f(x) = x2 + 1 1 0 83. 2 0 4 f(x) = x2 + 8x + 16 x2 + 4x – 5 x y 89. x y 0 2 –1 –2 2 4 y = x + 1 2 5 4 f(x) = x2 + 2x 2x – 1 91. x y 0 –3 –6 –3 3 f(x) = x2 – 9 x + 3 93. 8 8 0 f(x) = 2x2 – 5x – 2 x – 2 y = 2x – 1 x y 95. 3 6 4 0 f(x) = x2 – 1 x2 – 4x + 3 (1, –1) y x 97. y 4 4 0 x f(x) = (x2 – 9)(2 + x) (x2 – 4)(3 + x) (–3, 1.2) (–2, 1.25) 99. y 6 4 0 x f(x) = x 4 – 20x2 + 64 x4 – 10x2 + 9 85. 3 1 0 2 4 f(x) = 20 + 6x – 2x 2 8 + 6x – 2x2 x y 87. x y –3 –10 5 y = x – 3 f(x) = x 2 + 1 x + 3 0 101. ƒ1x2 = 1x - 321x + 22 1x - 221x + 22 , or ƒ1x2 = x 2 - x - 6 x2 - 4 103. ƒ1x2 = x - 2 x1x - 42 , or ƒ1x2 = x - 2 x2 - 4x 105. ƒ1x2 = -x1x - 22 1x - 122 , or ƒ1x2 = -x 2 + 2x x2 - 2x + 1 107. Several answers are possible. One answer is ƒ1x2 = 1x - 321x + 12 1x - 122 . 109. f(x) = −4.1 −2.6 8.1 10.6 x + 1 x − 4 ƒ11.252 = -0.81 111. f(x) = −4.1 −6.6 6.1 6.6 x2 + 2x 2x − 1 ƒ11.252 = 2.7083 113. (a) 26 per min (b) 5 park attendants For r = x, y = T(x) = y = 0.5 −0.4 25 1 40 2x − 25 2x2 − 50x 115. (a) 52 mph y = d(x) y = 300 −200 20 700 70 (b) x d1x2 x d1x2 20 34 50 273 25 56 55 340 30 85 60 415 35 121 65 499 40 164 70 591 45 215 (c) It more than doubles. Compare the values of d1202 and d1402, for example. (d) It would be linear. 117. All answers are given in tens of millions. (a) $65.5 (b) $64 (c) $60 (d) $40 (e) $0 119. y = 1 120. 1x + 421x + 121x - 321x - 52 121. 1x - 121x - 221x + 221x - 52 122. ƒ1x2 = 1x + 421x + 121x - 321x - 52 1x - 121x - 221x + 221x - 52 123. (a) x - 5 (b) 5 124. 1-4, 02, 1-1, 02, 13, 02 125. 10, -32 126. x = 1, x = 2, x = -2 127. Q7 { 2241 6 , 1R 128. x y 25 3 –3 –5 4 x = –2 x = 1 x = 2 y = 1 f(x) = x 4 – 3x3 – 21x2 + 43x + 60 x4 – 6x3 + x2 + 24x – 20 (5, )9 7 Chapter 3 Quiz [3.1] 1. (a) x y 1 –1 –3 0 f(x) = –2(x + 3)2 – 1 vertex: 1-3, -12; axis: x = -3; domain: 1-∞, ∞2; range: 1-∞, -14; increasing on 1-∞, -32; decreasing on 1-3, ∞2 (b) x y 2 –5 0 f(x) = 2x2– 8x + 3 vertex: 12, -52; axis: x = 2; domain: 1-∞, ∞2; range: 3-5, ∞2; increasing on 12, ∞2; decreasing on 1-∞, 22 2. (a) s1t2 = -16t2 + 64t + 200 (b) between 0.78 sec and 3.22 sec
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