Section 5.3 AN37 77. (a) f x x 2 1 5 3 ( ) = + − f f x f x x x x x f f x f x x x x x 2 2 2 2 2 2 2 2 2 2 1 5 3 5 3 5 3 3 3 3 3 1 1 3 5 3 5 3 5 5 5 5 5 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = += +−= +−= = = − = − + = − + = = − − − (b) Domain of f f Range of All Real Numbers; 1 = = − Domain of f f Range of All Real Numbers 1 = = − 79. (a) f x x x 3 2 1, 2 1( ) = − + ≥ − ( ) ( ) ( ) [ ] [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = − + = − + − + = − + = ⋅ − + = − + = = − += − +−+= − +=⋅ − + = − + = − − − f f x f x x x x x x f f x f x x x x x x 3 2 1 1 9 3 2 1 1 2 1 9 3 2 2 1 9 9 2 2 2 2 1 9 1 2 3 1 9 1 2 2 1 3 1 9 1 1 3 1 3 1 1 1 1 1 2 2 1 1 2 2 2 (b) Domain of f f x x Range of 1 ; 1 { } = = ≥ − Domain of f f x x Range of 2 1 { } = = ≥ − 81. (a) 0 (b) 2 (c) 0 (d) 1 83. 7 85. [ ) [ ) − ∞ ∞ − − f f Domain of : 2, ; range of : 5, 1 1 87. [ )∞ − − g g Domain of : 0, ; range of : 1 1 , 0 ( ] −∞ 89. Increasing on the interval f f 0, 5 [ ] ( ) ( ) 91. f x m x b m 1 , 0 1( ) ( ) = − ≠ − 93. Quadrant I 95. Possible answer: f x x x , 0, ( ) = ≥ is one-to-one; f x x x , 0 1( ) = ≥ − 97. (a) r d d 90.39 6.97 ( ) = + (b) r d r r r r d r d d d d 6.97 90.39 90.39 6.97 6.97 6.97 6.97 90.39 6.97 90.39 90.39 90.39 ( ( )) ( ( )) = − + = = = ⋅ + − = + − = (c) 56 miles per hour 99. (a) 77.6 kg (b) h W W W 50 2.3 60 88 2.3 ( ) = − + = + (c) h W h h h h W h W W W W 50 2.3 60 88 2.3 2.3 2.3 50 2.3 88 2.3 60 50 88 138 ( ) ( ( )) ( ) ( ( )) = + − + = = = + + − = + + − = (d) 73 inches 101. (a) g g 47,150 100,525 { } < ≤ (b) T T 5426 17,168.50 { } < ≤ (c) g T T 5426 0.22 47,150 ( ) = − + Domain: T T 5426 17,168.50 { } < ≤ Range: g g 47,150 100,525 { } < ≤ 103. (a) t represents time, so t 0. ≥ (b) t H H H 100 4.9 100 4.9 ( ) = − − = − (c) 2.02 seconds 105. f x dx b cx a f f a d ; if 1 1 ( ) = − + − = = − − − 107. (a) Domain: , ; ( ) −∞ ∞ Range: , 3 4, ( ) [ ) −∞ ∪ ∞ (b) ( ) = − < − ≥ ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ −f x x x x x 3 2 if 3 4 3 if 4 1 (c) Domain: , 3 4, ; ( ) [ ) −∞ ∪ ∞ Range: , ( ) −∞∞ 111. No 115. xh h h 6 3 7 2 + − 116. Zeros: 5 13 6 , 5 13 6 ; − − − + x-intercepts: 5 13 6 , 5 13 6 ; − − − + Vertex: 5 6 , 13 12 ; ( ) − − minimum; concave up 117. y 5 −5 x 3 −4 118. Domain: { } ≠ − ≠ x x x 3 2 , 2 ; Vertical asymptote: x 3 2 , = − Horizontal asymptote: y 3 = 119. x y 3 5 49 2 2 ( ) ( ) + + − = 120. y x2 7 = − − 121. Even 122. D y x y x 2 2 = − − 123. 16 − 124. x h x 2 2 2 3 2 3 + + + + 5.3 Assess Your Understanding (page 306) 8. (a) (i) 1 2 ; 1; 2 (ii) 1 3 ; 1; 3 (b) (i) 2; 1; 1 2 (ii) 3; 1; 1 3 (c) y-axis (d) decreasing; increasing (e) Horizontal line 9. (a) horizontally; right (b) (i) f x 2x 3 ( ) = + (ii) horizontally; left (c) vertically; up (d) (i) f x 2 3 x ( ) = − (ii) y 3 = − (iii) vertically; down (e) stretched; 1; 2; 4 (f) decreasing 10. exponential function; growth factor; initial value 11. a 12. T 13. T 14. a a 1 ; 1; 15. 4 16. F 17. b 18. c 19. (a) 8.815 (b) 8.821 (c) 8.824 (d) 8.825 21. (a) 21.217 (b) 22.217 (c) 22.440 (d) 22.459 23. 1.265 25. 0.347 27. 3.320 29. 149.952 31. Neither 33. Exponential; H x 5 4x ( ) = ⋅ 35. Exponential; f x 18 1 3 x ( ) ( ) = ⋅ 37. Linear; H x x2 4 ( ) = + 39. B 41. D 43. A 45. E 47. y 9 x 2.5 y 5 1 3 2 21, (0, 2) (1, 3) Domain: All real numbers Range: y y 1 { } > or 1, ( )∞ Horizontal asymptote: y 1 = y-intercept: 2 49. y 5 x 2.5 (1, 1) (2, 3) 1 3 0, y 5 0 Domain: All real numbers Range: y y 0 { } > or 0, ( )∞ Horizontal asymptote: y 0 = y-intercept: 1 3 51. y 7 x 2.5 (0, 3) 3 2 1, y 5 0 (21, 6) Domain: All real numbers Range: y y 0 { } > or 0, ( )∞ Horizontal asymptote: y 0 = y-intercept: 3 53. y 10 x 2.5 y 5 0 (0, 21) (21, 1) 5 3 1, 2 y 5 22 Domain: All real numbers Range: y y 2 { } >− or 2, ( ) − ∞ Horizontal asymptote: y 2 = − y-intercept: 1−
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