College Algebra Final Review Sheet

ALGEBRA FOR CALCULUS 3 b) axis of symmetry: x = FINAL REVIEW SHEET 9. x = -5 18. a) x构1, x 6 OR 2 ANSWERS Fall 2010 10. y = 22 (- , 1) 去 ( 1,6) (6, ) c) Since the leading coefficient is � � 3 positive, the function has a 32. Quotient: Q( x )= x - 2 x + 4 1. a) F; {- 2,0,1,2,7} ; 11. P( n )= 100000 - 350 n 25- 3x minimum. The minimum value R( x )= 0 b) Remainder: (x+ 1)(6 - x ) 7 {- 7, - 4, - 2,2,7} is - 12. a) -5 2 33. P(- 3) = 54 b) F; (-ゥ , ) ; [0, ) b) 4 Not a factor 19. a) f° g = 1+ 2 x ; c) 3.5 28. a) t =1.875 seconds c) F; (-ゥ , ) ; (-ゥ , ) g° f = 1+ 2x b) Max height is 86.25 ft. 1 1 1 13. 北1, , 北 , , d) NF; [0, ) ; (-ゥ , ) b) domain of f° g = [ 0, ) 2 4 5 29. odd 34. a) e) F; (-ゥ , ) ; (-ゥ , ) 轹 1 1 1 2 domain of g° f = - , 北, , 北 2, 滕 2 30. 10 20 5

2. a) f (1)= - 2 Zeros Mult at x-axis 2 0 3 cross 北1, 2, 北 3, 4, b) f (- 1) = 2 20. f° g = 2x- 6 x + 11; -3 2 tangent g° f = 4x2 - 2 x + 3 b) 1 3 c) f (0)= 0 14. a) Increasing: (- 10, - 8), ( - 2,1) 4 1 cross 北6, 12, , 21. origin 2 2 x @ -1.2 b) Decreasing: (- 8, - 7), (1,9) -1 4 tangent d) 3 values: x @ -.6 c) Constant: (- 7, - 2) 22. a) Neither 1 1 x @1.5 35. a) , b) Neither 31. 2 3 3 15. a) A( x )= - x2 + 180 x Zeros Mult at x-axis 2 3. a) f (- 4) = 24 2 c) Even b) ,i ,- i 1 1 cross 3 b) f (0)= 0 b) Domain: (0, 120) 23. a) y= x -2 - 3 -2 2 tangent 2 c) 2, 1 2i , c) f(- x ) = 2 x - 2 x 2 2 1 cross 2 b) y= -2 x + 5 5 3 d) 2x- 10 x + 12 16. a) [2,10] [0,7] [2,7] d) 1, i 1 e) 2x2+ 4 xh + 2 h 2 + 2 x + 2 h b) c) y = + 2 End behavior: 2 2 3x f) 4x+ 2 h + 2 (degree is even and leading coefficient e) q( x )= ( x - 5)( 2 x - 1) ( x + 3) 2 is negative, so think about y= x 24. a) 13i b) -7i 4. a) (-ゥ , ) , x 3 reflected about x-axis) 骣 1 x , y � 36. a) f( x )= x ( x + 3)琪 x - 轹15 As 桫 2 b) - , 25. a) 18+ 13i 滕 2 As x� ギ, y - b) -4 - 5i 5 3 c) (- 4, ) =x3 + x 2 - x 1 1 2 2 x构1, x 5 c) - i Intervals Test value + or - d) 2 2 (-� , 2) h(- 3) = - 10 - g( x )= ( x + 8)( x - 3 i )( x + 3 i ) 骣 4 d) -1 b) e) 琪- , (- 2,1) h(0)= - 4 - 3 2 桫 3 =x +8 x + 9 x + 72 (1,2) + -1 22 骣3 49 c) 26. a) h琪 = h( x )= ( x + 5) x - 3 5. a) D: [3, ) ; R:[2, ) 3 桫2 32 ( ) ゥ - c) x + 3 b) D: (- , ) ; R: (0, ) 5 7 (2, ) h(3)= - 25 ( ) b) - i =x3 +5 x 2 - 3 x - 15 c) D: [- 3,3] ; R:[0,3] 2 2

6. $ 161.4 million per year

1 10 7. x-3 y = - 10 or y = x + 3 3 2 27. f( x )= 2 x -3 - 7 1 7 ( 2) 2 8a) x+2 y = 7 or y = - x + 17. a) [ 0,2] 2 2 骣3 7 b) x + 2 - x a) vertex: 琪 ,- 8b) 2x- y = - 6 or y = 2 x + 6 桫2 2 12

37. 10 56.

8 Vert. asymp. Hor. asymp 6 Vertex Focus Direct. 4 a) x = 8 y = 0 2 a) x =1 2 -10 -5 5 10 15 (0,0) (-1 2,0) b) x = -5 y =1 -2 -4 c) x= -1, x = - 4 y = 0 -6 b) (-2,1) (-2, - 1 2) y = 5 2 -8 d) x=5, x = - 5 None 48. a) 3ln(x )+ 2ln( y ) - ln( z ) c) 骣 17 1 (-4, - 1 2) x = 44. a) 琪-, - 桫 4 2 -9 2 38. a) No zeros b) ln(6)- 2

14 b) 2 5 12 c) 3+ 4logb - log m - log n a) 10 a a2 a 8 c) -3 6

2 2 d) 0, 1,- 3 49. ln3 x- 3 ( x + y ) ( ) -15 -10 -5 5 10 3 b) -2 39. a) (-�, 去 2 4, ) 2 -4 -6  1 50. a) 3 b) 50 c) 6- 4x (0,0) -8 -4 -2 2 4 6 8 10 -10 -�, � 2 1,2 -1 1 -12 b) (  51. a) 10 -2 4 8

-3 b) 6 c) 轾- 3, 3去 2, ) -4 b) 5 4 2 臌 -5

-15 -10 -5 5 10 15 -6 5 c) -2 d) (- ,5) 2 -4 6 -6 c) 5 ln10.4 -8 -10 e) (1,2) 去 5, ) 4 d) 1.171 (0,3) -12 3 2 -14

1 12 e) 6 -18

10 40. a) Yes -4 -2 2 4 6 8 10

8 b) Yes -1 ln 2 c) 6 -2 52. .087 c) Yes 8 4 -3

2 d) No -4

53. a) 6% -15 -10 -5 5 10 15 3x - 5 -2 41. a) y = 2 45. $22,099.36 b) A( t )= 8000 e.06t -4 -6 1- 4x -8 b) y = c) $14, 577 -10 3 -12 2 a) 5 ln 2 c) x-2, x > 0 d) 11.55 years b) - 2 0.06 57. Center: (-3,5) c) - 4 Radius: 34 42. You need to show that f( g ( x )) = x 46. d) 2 and that g( f ( x )) = x . 3 58. e) 2 3 Cntr Vertices Foci 43. a) 8 a) (0,0) (0,6) (0, 11) 6 k � 0.175;

4 54. a) -0.175t (0,- 6) P( t )= 3395 e 0,- 11 2 ( ) 47.Domain is (-5, ) b) $103 -10 -5 5 10 b) (0,0) (0,4) 0, 7 -2 ( ) Range is (-ゥ, ) 10 -4 1 0,- 4 9 ln ( ) b) 8 -6 Vert. asymptote: x = -5 c) 2 3.96 years (0,- 7) 7 -8 -0.175 6 -4,0 c) 5 Intercept: ( ) (-3,5) (-3,11) -3,5 + 11 4 ( ) (4,3) 3 55. a) b) 4 2 2 41 3 (-3, - 1) 1 -3,5 + 11

-6 -4 -2 2 4 6 8 10 12 14 ( )

-4 d) (5,- 2) 7,- 2 e) ellipse 1000 ( ) (5+2 , - 2) b) f) hyperbola 11 (3,- 2) 5-2 , - 2 ( ) 1 ft or 6 in 61. 2 b) Does not exist 62. 0.7 ft a) 8 $36,749.54 6 74. 63. 225

2 307 5 -10 -5 5 10 64. a) 75. a) ft -2 256 10 210

-6 c) 6 b) Approximately 6.7ft -8 b) -52,428 4

2 6 b) -15 -10 -5 5 10 15 4 -2 65. a) 7k

-4 2 k=1

-8 -5 5

-10 -2 n k 2 -4 b) (-1) k 10 k=2 -6 d) 8 c) 12 6 66. -41

6 -15 -10 -5 5 10 67. -43 4 -2

2 -4 3 -10 -5 5 10 -6 68. -2 -8 2

-4 69. 10,000

60. a) ellipse d) 4 b) hyperbola c) parabola 70. 136 marchers 2 d) circle 71. a) 6561 -5 5 10 Cntr Vertices Foci.

-2 a) 96 a) (0,0) (5,0) ( 34,0) -4 c) -0.0008 59. (-5,0) (- 34,0) 10 d) -1 a) 8 b) (0,0) (4,0) 41,0 6 ( ) 4 (-4,0) 341 21 122 72. or 10 (- 41,0) 32 32 10 -20 -15 -10 -5 5 10 15 20

-28 c) (-1, - 3) (-1, - 1) -1, - 3 + 2 5 -4 6 ( )

-6 4 49 -8 2 (-1, - 5) 73. a) (-1, - 3 - 2 5) 4 -15 -10 -5 5 10 15 -2 d) (-3,1) (-5,1) -3 + 13 ,1 -4 ( )

b) -6 -1,1 -8 ( ) (-3 - 13 ,1) -10