AN38 Answers: Chapter 5 55. y 8 x 6 y 5 2 33 16 21, (2, 6) (1, 3) Domain: All real numbers Range: y y 2 { } > or 2, ( )∞ Horizontal asymptote: y 2 = y-intercept: 9 4 57. y 8 x 2.5 y 5 2 (2, 5) (0, 3) 7 3 22, Domain: All real numbers Range: y y 2 { } > or 2, ( )∞ Horizontal asymptote: y 2 = y-intercept: 3 59. y 8 x 5 y 5 0 (0, 1) (21, e) (22, e2) 1 e 1, Domain: All real numbers Range: y y 0 { } > or 0, ( )∞ Horizontal asymptote: y 0 = y-intercept: 1 61. y 8 x 5 y 5 0 (0, e2) (21, e) (22, 1) 23, 1 e Domain: All real numbers Range: y y 0 { } > or 0, ( )∞ Horizontal asymptote: y 0 = y-intercept: e2 63. y 8 x 5 y 5 5 (0, 4) Domain: All real numbers Range: y y 5 { } < or , 5 ( ) −∞ Horizontal asymptote: y 5 = y-intercept: 4 65. y 5 x 5 (0, 1) y 5 2 Domain: All real numbers Range: y y 2 { } < or , 2 ( ) −∞ Horizontal asymptote: y 2 = y-intercept: 1 67. 5{ } 69. 4 { } − 71. 2{ } 73. 7 2{ } 75. 2, 0, 2 { } − 77. 3{ } 79. 1, 7 { } − 81. 4, 2 { } − 83. 4 { } − 85. 1, 2 { } 87. 1 49 89. 1 4 91. 5 93. f x 3x ( ) = 95. f x 6x ( ) = − 97. f x 3 2 x ( ) = + 99. (a) 16; 4, 16 ( ) (b) 4; 4, 1 16 ( ) − − 101. (a) 9 4 ; 1, 9 4 ( ) − (b) 3; 3, 66 ( ) 103. (a) 60; 6, 60 ( ) − (b) 4; 4, 12 ( ) − − (c) 2− 105. y 8 x 5 (0, 1) (1, e) (21, e) (2, e2) (22, e2) Domain: , ( ) −∞ ∞ Range: 1, [ )∞ Intercept: 0, 1 ( ) 107. y 3 x 5 y 5 0 (0, 21) e2 1 e2 2, 2 1 22, 2 1 e 1, 2 1 e 21, 2 Domain: , ( ) −∞ ∞ Range: 1, 0 [ ) − Intercept: 0, 1 ( ) − 109. (a) 74% (b) 47% (c) Each pane allows only 97% of light to pass through. 111. (a) $18,586 (b) $9877 (c) As each year passes, the sedan is worth 90% of its value the previous year. 113. (a) 30% (b) 9% (c) Each year only 30% of the previous survivors survive again. 115. 3.35 mg; 0.45 mg 117. (a) 0.632 (b) 0.982 (c) 1 (d) 1 0 0 40 y = 1−e−0.1t (e) About 7 min 119. (a) 0.0516 (b) 0.0888 121. (a) 70.95% (b) 72.62% (c) 100% 123. (a) 5.41 amp, 7.59 amp, 10.38 amp (b) 12 amp (d) 3.34 amp, 5.31 amp, 9.44 amp (e) 24 amp (c), (f) I 30 t 5 I2 (t) 5 24(1 2 e 20.5t) I1 (t) 5 12(1 2 e 22t) 125. 36 127. Final Denominator Value of Expression Compare Value to ≈ e 2 718281828 . 1 1 + 2.5 e 2.5 < 2 2 + 2.8 e 2.8 > 3 3 + 2.7 e 2.7 < 4 4 + 2.721649485 e 2.721649485 > 5 5 + 2.717770035 e 2.717770035 < 6 6 + 2.718348855 e 2.718348855 > 135. 1, 2 { } 137. 59 minutes 141. a a a 1 x x x 1 ( ) ( ) = = − − 142. , 5 2, 2 ( ] [ ] −∞ − ∪ − 143. 2, ( )∞ 144. f x x x 2 12 13 2 ( ) = − + − 145. (a) y x 5 5 (1, 0) (0, 23) (22, 23) (23, 0) (21, 24) x 5 21 (b) Domain: , ( ) −∞ ∞; Range: 4, [ ) − ∞ (c) Decreasing: , 1 ( ] −∞ − ; Increasing: 1, [ ) − ∞ 146. 3 2{ } 147. x y 1 2 2 + = 148. 16, 144 { } 149. $1050 150. x 3 3 − ≤ ≤ 151. x h 4 2 7 + − 129. f A B a a a f A f B A B A B ( ) ( ) ( ) + = = ⋅ = ⋅ + 131. f x a a f x x x α ( ) [ ] ( ) ( ) = = = α α α 133. (a) f x e e e e e e f x 1 2 1 2 1 2 x x x x x x ( ) ( ) ( ) ( ) ( ) − = + = + = + = ( ) − −− − − (c) x x cosh sinh 2 2 ( ) ( ) − e e e e e e e e 1 2 1 2 1 4 2 2 1 4 4 1 x x x x x x x x 2 2 2 2 2 2 ( ) ( ) [ ] = ⎡ + ⎣ ⎢ ⎤ ⎦ ⎥ − ⎡ − ⎣ ⎢ ⎤ ⎦ ⎥ = + + − + − = ⋅ = − − − − (b) 6 26 21 6 y = 1 2 (ex + e−x) 5.4 Assess Your Understanding (page 321) 3. (a) decreasing; increasing (b) 1; 0; 1 − (c) 1; 0; 1 − (d) 1; 0; 1− 4. (a) horizontally; right (b) horizontally; left (c) x 5 = (d) vertically; up (e) y 2 = − (f) increasing (g) 5, ; 5, ( ) ( ) ∞ ∞ 5. x x 0 { } > or 0, ( )∞ 6. a a 1 ; 1; 7. 1 8. F 9. T 10. a 11. c 12. b 13. 2 log 9 3 = 15. 2 log 1.6 a = 17. x log 7.2 2 =
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