{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}