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ch 0 answers for hw - Chapter 0 Functions 0.1 1. 2. 3. 4....

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Chapter 0 Functions 0.1 Functions and Their Graphs 1. 2. 3. 4. 5. 6. 7. [2, 3) 8. 3 1, 2 !" # $% &’ 9. [–1, 0) 10. [–1, 8) 11. ( ) ,3 #* 12. ) 2, + * , 13. 2 ( ) 3 f x x x -# 2 (0) 0 3(0) 0 f - # - 2 (5) 5 3(5) 25 15 10 f - # - # - 2 (3) 3 3(3) 9 9 0 f - # - # - 2 ( 7) ( 7) 3( 7) 49 21 70 f # - # # # - . - 14. 2 ( ) 9 6 f x x x - # . 2 (0) 9 6(0) 0 9 0 0 9 f - # . - # . - 2 (2) 9 6(2) 2 9 12 4 1 f - # . - # . - 2 (3) 9 6(3) 3 9 18 9 0 f - # . - # . - 2 ( 13) 9 6( 13) ( 13) 9 78 169 256 f # - # # . # - . . - 15. 32 ( ) 1 f x x x x - . # # (1) 1 1 1 1 0 f - . # # - ( 1) ( 1) ( 1) ( 1) 1 0 f # - # . # # # # - 1 1 1 1 9 1 2 2 2 2 8 f ! " ! " ! " ! " - . # # - # $ % $ % $ % $ % & ’ & ’ & ’ & ’ ( ) 1 f a a a a - . # # 16. ( ) 3 g t t t t - # . (2) 2 3(2) 2 8 12 2 2 g - # . - # . - # 1 1 1 1 3 2 2 2 2 1 3 1 11 8 4 2 8 g ! " ! " ! " ! " # - # # # . # $ % $ % $ % $ % & & & & - # # # - # 2 2 2 2 3 3 3 3 3 8 12 2 10 .37037 27 9 3 27 ! " ! " ! " ! " - # . $ % $ % $ % $ % & ’ & ’ & ’ & ’ - # . - # / # g ( ) 3 g a a a a - # . 17. () (1 ) s hs s - . 11 22 3 1 2 2 23 1 h - - - . 33 1 3 2 2 3 3 2 1 h ## # - - - # .# ( 1) 1 ( 2 aa ha .. . - - . . . 18. 2 2 1 x fx x - # ( ) 2 1 1 2 4 21 1 4 2 1 1 f - - - # # # ( ) 2 1 1 2 4 1 4 2 1 1 f # # - - - # # 2 2 ( 2 1 ( ( 1 ( 2 1) 1 2 a a a fa a a a . . . . - - . # . . # - . 19. 2 ( ) 2 f x x x 2 ( ( 2( ( 2 2 2 1 f a a a a a a a . - . # . - . . # # - # 2 ( 2) ( 2) 2( 2) ( 4 4) 2 4 2 f a a a a a a a a . - . # . - . . # # - .
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2 Chapter 0: Functions 20. 2 ( ) 4 3 f x x x - . . 2 2 2 ( 1) ( 4( 3 ( 2 (4 4) 3 2 f a a a a a a aa # - # . # . - # . . # . -. 2 2 2 ( 2) ( 2) 4( 2) 3 ( 4 4) (4 8) 3 1 f a a a a a a a # - # . # . - # . . # . -# 21. a. f (0) represents the number of fax machines sold in 1990. b. 2 1 (2) 50 4(2) (2) 2 50 8 2 60 f - . . - . . - 22. 100 ( ) , - . x Rx bx x 0 a. b = 20, x = 60 100(60) (60) 75 20 60 R -- . The solution produces a 75% response. b. If R (50) = 60, then 100(50) 60 50 60 3000 5000 100 3 b b b - . .- - This particular frog has a positive constant of 33.3. 23. 8 () ( 1)( 2) x fx xx - ## all real numbers such that x 1, 2 or ( ) ( ) ( ) , 1 1,2 2, #* # 0 # 0 * 24. 1 ft t - all real numbers such that t > 0 or ( ) 0, * 25. 1 3 gx x - # all real numbers such that x < 3 or ( ) ,3 #* # 26. 4 ( 2) - . all real numbers such that x 0, –2 or ( ) ( ) ( ) , 2 2,0 0, #* # 0 # 0 * 27. function 28. not a function 29. not a function 30. not a function 31. not a function 32. function 33. 1 34. –1 35. 3 36. 0 37. positive 38. negative 39. positive 40. yes 41. –1, 5, 9 42. 1 2 1 2 1,5 , 9, #* 43. .03 44. .03 45. .04 46. 3 47. 1 ( ) 2 2 f x x x !" - # . $% &’ 1 25 (3) 3 (3 2) 22 f - # . - Thus, (3, 12) is not on the graph. 48. f ( x ) = x (5 + x )(4 – x ) f (–2) = –2(5 + (–2))(4 – (–2)) = –36 So (–2, 12) is not on the graph. 49. 2 31 1 x x # - . ( ) 1 1 2 2 25 1 4 2 12 35 1 g # - - - . So , ! " $ % & is on the graph. 50. 2 ( 4) ( 2) x x . - . ( ) 2 2 40 3 9 28 3 3 4 33 2 g . - - - . So , ! " $ % & is on the graph. 51. 3 f x x - 3 ( ( f a a . - . 52. 5 f x x x 5 (2 ) (2 ) (2 ) 5 (2 ) 1 4 (2 ) 2 f h h h h h h hh . - # . . # . # # ..
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Section 0.1: Functions and Their Graphs 3 53. for 0 2 () 1 for 2 5 xx fx 3 45 6 - 7 . 4 4 6 8 (1) 1 1 f -- f (2) = 1 + 2 = 3 f (3) = 1 + 3 = 4 54. 2 1 for 1 2 for 2 x x 3 44 6 - 7 6 5 8 1 1 1 f ; 1 (2) 2 f - 2 (3) 3 9 f 55. 2 for 2 ( ) 1 for 2 2.5 4 for 2.5 f x x x 9 3 5 6 - . 4 4 7 6 5 8 2 f 99 f (2) = 1 + 2 = 3 f (3) = 4(3) = 12 56. 2 3 for 2 4 ( ) 2 for 2 3 5 for 3 x x f x x x 3 5 6 # 6 - 4 5 7 6 #4 6 8 3 1 41 f # f (2) = 2(2) = 4 2 (3) 3 5 4 2 f - # - - 57. .06 for 50 300 ( ) .02 12 for 300 600 .015 15 for 600 f x x x 3 6 - . 5 4 7 6 .: 8 58. 59. 60. Entering Y 1 = 1/X + 1 will graph the function 1 ( ) 1 x -. . In order to graph the function 1 1 x - . , you need to include parentheses in the denominator: Y 1 = 1/(X + 1) . 61. Entering Y 1 = X ^ 3 / 4 will graph the function 4 x ; - . In order to graph the function 34 yx - , you need to include parentheses in the exponent: Y 1 = X ^ (3/4) . 62. Y 1 = X^3 - 33X^2 +120X+1500 [-8, 30] by [-2000, 2000] 63. Y 1 = -X^2+2x+2 [-2, 4] by [-8, 5] 64. Y 1 = (X+1)^(1/2) [0, 10] by [-1, 4] 65. Y 1 = 1/(X^2+1) [-4, 4] by [-.5, 1.5]
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4 Chapter 0: Functions 0.2 Some Important Functions 1.
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ch 0 answers for hw - Chapter 0 Functions 0.1 1. 2. 3. 4....

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