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ss_answers - Answers 3.1 Exercises 1 D 2 F 3 A 4 H 5 B 6 C...

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Answers 3.1 Exercises 1. D 2. F 3. A 4. H 5. B 6. C 7. E 8. G 9. D 10 A 11. B 12. C 16. Minimum value;-18 17. Maximum value;13 18. $500; $1 , 000 , 000 19. 40; $400 20. (a) R ( x ) = - 1 6 x 2 + 100 x (b) $13 , 333 (c) 300; $15 , 000 (d) $50 21. (a) A ( x ) = - x 2 + 200 x (b) A is the largest when x = 100yd (c) 10 , 000sq yd 22. 2,000,000 square meters 23. 4 , 166 , 666 . 7 m 2 Answers 3.3 Exercises 1. No; x is raised to the - 1 power. 2. No; x is raised to the 2 / 3 power. 3. Yes; degree 4 4. f ( x ) = x 3 - 3 x 2 - x + 3 for a = 1 5. f ( x ) = x 4 - 15 x 2 + 10 x + 24 for a = 1 6. 7,multiplity 1; - 3, multiplicty 2; graph touches the x-axis at - 3 and cross it at 7 7. - 1 / 2,multiplity 2;graph touches the x-axis at - 1 / 2 8. No real zeros; graph neither cross nor touches the x-axis 9. b x-intercepts:-4,0,2;y-intercept:0 (c) -4,0,2:Odd (d) y = x 3 (e) 2 (f) Local minimum:(1.10,- 5.05);Local maximum:(-2.43,16.90) 10. b x-intercepts:-1,0,3;y-intercept:0 (c) -4,3:Odd;0:Even (d) y = x 4 (e) 3 (f) Local minima:(2.19,- 12.39),(-0.69,-0.54);Local maximum:(0,0) 11. b x-intercepts:-1.26,0.20,1.26;y-intercept:-0.31752 (c) -1.26,0.20,1.26:Odd (d) y = x 3 (e) 2 (f) Local minimum:(0.66,-0.99);Local maximum:(-0.80,0.57) 12. b x-intercepts:-4.78,0.45,3.23;y-intercept:-3.1264785 (c) -4.78,3.23:Odd;0.45:Even (d) y = x 4 (e) 3 (f) Local minima:(-3.32,-135.92),(2.38,-22.67);Local maximum:(0.45,0) Answers 3.4 Exercises 1. No; f (3) = 61 2. Yes; f ( - 2) = 0 3. 4; ± 1, ± 1 / 3 4. 5; ± 1, ± 2 , ± 4, ± 1 / 2 5. -1 and 1 6. - 10 and 10 7. - 3 , - 1 , 2; f ( x ) = ( x + 3)( x + 1)( x - 2) 8. - 5 . 9 , - 0 . 3 , 3 9. {- 1 , 2 } 10. { 1 / 3 , 5 , - 5 } 1
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11. f (0) = - 1; f ( - 1) = 10;Zero:0.22 12. f (1 . 4) = - 0 . 17536; f (1 . 5) = 1 . 40625;Zero:1.41 13. k = 5 Answers 3.5 Exercises 1. - 6 - 11 i 2. 6 + 4 i 3. 10 - 5 i 4. 6 / 5 + 8 / 5 i 5. 1 - 2 i 6. 5 / 2 - 7 / 2 i 7. - 10 i 8. 0 9. 2 i 10. 5 i 11. {- 2 i, 2 i } 12. { 3 - i, 3 + i } 13. { 1 / 2 - 3 / 2 i, - 1 / 2 + 3 / 2 i } 14. {- 3 i, - 2 i, 2 i, 3 i } 15. Two complex solutions 16. A repeated real solution 17. 2 - 3 i 18. 6 19. 25 Answers 3.6 Exercises 1. 4 + i 2. 2 - i, - 3 + i 3. f ( x ) = x 4 - 14 x 3 + 77 x 2 - 2000 x + 208; a = 1 4. - 2 i ; 4 5. 3 + 2 i, - 2 , 5 6. 1 , - 1 / 2 - 3 / 2 i, - 1 / 2 + 3 / 2 i 7. 2 , 3 - 2 i, 3 + 2 i Answers 3.7 Exercises 1. All real numbers except - 1 / 2 and 3 2. All real numbers except 2 3. All real numbers 4. (graph 13) (a) Domain: { x | x 6 = 2 } ; Range: { y | y 6 = 1 } ; (b) (0,0); (c) y = 1; (d) x = 2; (e) None 11. Horizontal asymptote: y = 3; vertical asymptote: x = - 4 12. Horizontal asymptote: y = 0; vertical asymptote: x = 1, x = - 1 13. (1) Domain: { x | x 6 = 0 , x 6 = - 4 } ; (2) x-intercept:-1;no y-intercept; (3) No symmetry; (4) Vertical asymptote: x = 0 , x = - 4; (5) Horizontal asymptote: y = 0,intersected at ( - 1 , 0) 14. (1) Domain: { x | x 6 = - 3 , x 6 = 3 } ; (2) x-intercept:1; y-intercept:1/9; (3) No symmetry; (4) Vertical asymptote: x = 3 , x = - 3; (5) Oblique asymptote: y = x , intersected at (1 / 9 , 1 / 9) 15. (1) Domain: { x | x 6 = 1 , x 6 = - 2 , x 6 = 2 } ; (2) No x-intercept; y-intercept:3/4; (3) No symmetry; (4) Vertical asymptote: x = - 2, x = 1, x = 2; (5) Horizontal asymptote: y = 0,not intersected Answers 3.8 Exercises 1. { x | - ∞ < x < 0 or 4 < x < ∞} 2. { x | - ∞ < x < - 4 or 3 < x < ∞} 2
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3. { x | 1 < x < ∞} 4. { x | - ∞ < x < - 1 or 1 < x < ∞} 5. { x | - ∞ < x < 2 or 3 < x < 5 } Answers 4.1 Exercises 1. (graph 9) One-to-one; (graph 11) Not one-to-one 3. f ( g ( x )) = f (1 / 3( x - 4)) = x ; g ( f ( x )) = g (3 x + 4)) = x 4. f ( g ( x )) = (( x + 8) 1 / 3 ) 3 - 8 = x ; g ( f ( x )) = (( x 3 - 8) + 8) 1 / 3 = x 5. f ( g ( x )) = 2( 4 x - 3 2 - x )+3 4 x - 3 2 - x +4 = x ; g ( f ( x )) = 4( 2 x +3 x +4 ) - 3 2 - 2 x +3 x +4 = x 6. f - 1 ( x ) = x 4 - 1 2 f ( f - 1 ( x )) = 4( x 4 - 1 2 ) + 2 = x f - 1 f (( x )) = 4 x +2 4 - 1 2 = x Domain f = Range f - 1 = ( -∞ , ) Range f = Domain f - 1 = ( -∞ , ) 7. f - 1 ( x ) = ( x + 1) 1 3 f ( f - 1 ( x )) = (( x + 1) 1 3 ) 3 - 1 = x f - 1 f (( x )) = (( x 3 - 1) + 1) 1 3 = x Domain f = Range f - 1 = ( -∞ , ) Range f = Domain f - 1 = ( -∞ , ) 9. f - 1 ( x ) = 2 x +1 x f ( f - 1 ( x )) = 1 2 x +1 x - 2 = x f - 1 f (( x )) = 2( 1 x - 2 )+1 1 x - 2 = x Domain f = Range f - 1 = All real numbers except 2 Range f = Domain f - 1
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