01_M_GOLD_9004_12_ch00

# 01_M_GOLD_9004_12_ch00 - Chapter 0 Functions 0.1 1. 2. 3....

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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 fx 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 fx 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 (1 3 ) 9 6 3 ) (1 3 ) 9 78 169 256 f −= −+ =+ + = 15. 32 1 fx x x x =+−− (1) 1 1 1 1 0 f =+− ) ) ) 1 0 f −=− +− −−−= 11 1 1 9 1 22 2 2 8 f ⎛⎞ ⎛⎞ ⎛⎞ ⎛⎞ = ⎜⎟ ⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ ⎝⎠ ⎝⎠ 1 fa a a a 16. 3 gt t t t (2) 2 3(2) 2 8 12 2 2 g += −+= 1 1 3 2 2 131 1 1 842 8 g ⎞⎛ ⎞ ⎛ ⎞ ⎛ ⎞ + ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎠⎝ ⎠ ⎝ ⎠ ⎝ ⎠ =− − − =− 2 2 3 33 3 3 81 22 1 0 .37037 2 793 2 7 ⎛⎞ ⎛⎞ + ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ =−+ = −≈ g 3 ga a a a 17. ) s hs s = + 3 1 2 2 23 1 h == = + 1 3 2 2 3 3 2 1 h −− = = +− ) 1( 1 ) 2 aa ha ++ = + 18. 2 2 1 x 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 ) ) )1( 21 ) 1 2 a fa a + = = + 19. 2 2 x 2 ( 1) ( 2( (2 1 ) 2 2 1 a a a a += + − + =+ + = 2 ( 2) ( 2) 2( 2) (4 4 ) 2 4 2 a a a +=+ − + + = +

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2 Chapter 0: Functions 20. 2 () 4 3 fx x x =++ 2 2 2 (1 ) )4 )3 (2 1 ) ( 4 4 ) 3 2 fa a a aa a −= − + −+ =− + +− + =+ 2 2 2 ( 2) ( 2) 4( 2) 3 (4 4 ) ( 4 8 ) 3 1 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 ) ) x fx xx = −− all real numbers such that x 1, 2 or ( ) ( ) ( ) ,1 1 , 2 2 , −∞ − ∪ − 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 ) = + all real numbers such that x 0, –2 or ( ) ( ) ( ) ,2 2 , 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, 5 , 9, −∞ 43. .03 44. .03 45. .04 46. 3 47. 1 2 2 x x ⎛⎞ + ⎜⎟ ⎝⎠ 12 5 (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 35 1 g = + So , is on the graph. 50. 2 ) ) x x + = + ( ) 2 2 40 3 9 28 3 3 4 33 2 g + = + So , is on the graph. 51. 3 = 3 ) ) a += + 52. 5 x x 5 ) ) (2 ) 5( 2 ) 14 ) 2 fh h h hh h −+ + − − ++
Section 0.1: Functions and Their Graphs 3 53. for 0 2 () 1f o r 2 5 xx fx ≤< = +≤ (1) 1 1 f == f (2) = 1 + 2 = 3 f (3) = 1 + 3 = 4 54. 2 1 for 1 2 for 2 x x ≤≤ = < 1 1 1 f ; 1 (2) 2 f = 2 (3) 3 9 f 55. 2 for 2 1 f o r 2 2 . 5 4 for 2.5 x x π < =+ < 2 f ππ f (2) = 1 + 2 = 3 f (3) = 4(3) = 12 56. 2 3 for 2 4 2 f o r 2 3 5f o r 3 x x x x < =≤ < −≤ 3 1 41 f f (2) = 2(2) = 4 2 (3) 3 5 4 2 f =− = = 57.

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## This note was uploaded on 04/24/2010 for the course MATH 9374 taught by Professor Smith during the Spring '10 term at University of California, Berkeley.

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01_M_GOLD_9004_12_ch00 - Chapter 0 Functions 0.1 1. 2. 3....

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