Section 5.1 AN33 3. − i i 4, 5 , 5 4. { } − + 1, 5 61 6 , 5 61 6 5. Domain: { } ≠ − ≠ x x x 10, 4 ; asymptotes: = − = x y 10, 2 6. Domain: { } ≠ − x x 1 ; asymptotes: = − = + x y x 1, 1 7. y 5 x 5 (0, 23) (23, 0) (1, 0) x 5 21 y 5 x 1 1 8. Answers may vary. One possibility is ( ) = − − + f x x x x x 4 2 20 4 3 2 . 9. Answers may vary. One possibility is ( ) ( )( ) ( )( ) = − − − − r x x x x x 2 9 1 4 9 . 10. ( ) ( ) = = − f f 0 8; 4 36; Since ( ) ( ) = > = − < f f 0 8 0 and 4 36 0, the Intermediate Value Theorem guarantees that there is at least one real zero between 0 and 4. 11. { } ( ) ( ) < > −∞ ∪ ∞ x x x 3 or 8 ; , 3 8, 12. { } ( ] [ ] ≤− −≤ ≤ −∞− ∪− x x x 3 or 2 0 ; , 3 2, 0 Cumulative Review (page 269) 1. 26 2. { } ( ] [ ) ≤ ≥ −∞ ∞ x x x 0 or 1 ; , 0 or 1, 0 1 3. { } ( ) − < < − x x 1 4 ; 1, 4 21 4 4. ( ) = − + f x x3 1 y 5 x 5 (21, 4) 5. = − y x2 1 y 6 x 5 (3, 5) 6. y 10 x 10 (21, 21) (22, 28) (2, 8) (1, 1) 7. Not a functions; 3 has two images. 8. { } 0, 2, 4 9. { } ) ≥ ⎡ ∞ ⎢ ⎣ x x 3 2 ; 3 2 , 0 1 2 3 10. Center: ( ) −2, 1 ; radius: 3 y 5 x 2 (1, 1) (22, 4) (22, 1) (22, 22) (25, 1) 11. x-intercepts: −3, 0, 3; y-intercept: 0; symmetric with respect to the origin 12. = − + y x 2 3 17 3 13. Not a function; it fails the Vertical Line Test. 14. (a) 22 (b) − − x x5 2 2 (c) − − + x x5 2 2 (d) + − x x 9 15 2 2 (e) + + x h 2 5 15. (a) { } ≠ x x 1 (b) No; ( ) 2,7 is on the graph. (c) 4; ( ) 3, 4 is on the graph. (d) ( ) 7 4 ; 7 4 , 9 is on the graph. (e) Rational 16. y 8 x 8 (0, 7) , 0 7 3 17. y 6 x 3 x 5 1 (0, 1) (1, 21) 1 1 2 2 , 0 Ï 1 2 2 2 , 0 Ï 18. = − y x 6; 6 1 19. (a) x-intercepts: − − 5, 1, 5; y-intercept: −3 (b) No symmetry (c) Neither (d) Increasing: ( ] [ ) −∞ − ∞ , 3 and 2, ; decreasing: [ ] −3, 2 (e) Local maximum value is 5 and occurs at = − x 3. (f) Local minimum value is −6 and occurs at = x 2. 20. Odd 21. (a) Domain: { } ( ) > − − ∞ x x 3 or 3, (b) x-intercept: − 1 2 ; y-intercept: 1 (c) y 5 x 5 (2, 22) (0, 1) (2, 5) (23, 25) 2 , 0 1 2 (d) Range: { } ( ) < −∞ y y 5 or , 5 22. y 8 x 2 (0, 2) (21, 5) (22, 2) 23. (a) ( )( ) + = − − f g x x x9 6 2 ; domain: all real numbers (b) ( ) ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ = − + − − f g x x x x 5 1 4 7 2 ; domain: { } ≠ − x x 7 4 24. (a) ( ) = − + R x x x 1 10 150 2 (b) $14,000 (c) 750; $56,250 (d) $75 CHAPTER 5 Exponential and Logarithmic Functions 5.1 Assess Your Understanding (page 277) 4. composite function; f g x ( ) ( ) 5. F 6. c 7. a 8. F 9. (a) −1 (b) −1 (c) 8 (d) 0 (e) 8 (f) −7 11. (a) 4 (b) 5 (c) −1 (d) −2 13. (a) 98 (b) 49 (c) 4 (d) 4 15. (a) 197 (b) − 835 2 (c) 197 (d) − 3 2 17. (a) 2 5 (b) 5 2 (c) 1 (d) 0 19. (a) 1 25 (b) 1 13 (c) 1 (d) 81 730 21. (a) + 3 4 1 3 (b) 1 (c) 6 5 (d) 0 23. (a) ( )( ) = + f g x x8 3; all real numbers (b) ( )( ) = + g f x x8 12; all real numbers (c) ( )( ) = + f f x x4 9; all real numbers (d) ( )( ) = g g x x 16 ; all real numbers 25. (a) ( )( ) = − f g x x3 1; 2 all real numbers (b) ( )( ) = − + g f x x x 9 6 1; 2 all real numbers (c) ( )( ) = − f f x x9 4; all real numbers (d) ( )( ) = g g x x ;4 all real numbers 27. (a) ( )( ) = + + f g x x x8 16; 4 2 all real numbers (b) ( )( ) = + g f x x 4; 4 all real numbers (c) ( )( ) = f f x x ;4 all real numbers (d) ( )( ) = + + g g x x x8 20; 4 2 all real numbers 29. (a) f g x x x x x x 3 2 ; 0, 2 ( )( ) { } = − ≠ ≠ (b) g f x x x x 2 1 3 ; 1 ( )( ) ( ) { } = − ≠ (c) f f x x x x x x 3 1 4 ; 1, 4 ( )( ) ( ) { } = − − ≠ ≠ (d) g g x x x x ; 0 ( )( ) { } = ≠ 31. (a) f g x x x x x 4 4 ; 4, 0 ( )( ) { } = + ≠ − ≠ (b) g f x x x x x x 4 1 ; 0, 1 ( )( ) ( ) { } = − − ≠ ≠ (c) f f x x x x ; 1 ( )( ) { } = ≠ (d) g g x x x x ; 0 ( )( ) { } = ≠
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