Solve for x



COLLEGE ALGEBRA FINAL REVIEW

Similar problems can be found in Chapters P-4 of your textbook: College Algebra Essentials, 4th Edition by Blitzer.

Solve.

1) [pic]

2) [pic]

3) [pic]

4) [pic]

5) [pic]

6) [pic]

7) [pic]

8) [pic]

9) [pic]

10) [pic]

11) solve for L [pic]

12) [pic]

13) a) [pic][pic]

b) [pic]

14) [pic]

15) [pic]

16) [pic]

17) [pic]

18) [pic]

19) [pic]

20) [pic]

21) [pic]

Write as a single logarithm and simplify, if possible.

22) [pic]

23) [pic]

24) Write as the sum of difference of logarithms; express powers as factors. [pic]

Simplify the following:

25) [pic]

26) [pic]

27) [pic]

28) [pic]

29) [pic]

30) [pic]

31) [pic]

32) [pic]

33) [pic]

34) [pic]

35) [pic]

36) [pic]

37) [pic]

38) [pic]

39) [pic]

40) [pic]

Evaluate to 3 decimal places.

41) [pic]

42) [pic]

43) [pic]

Given: [pic]. Find the following to 3 decimal places.

44) [pic]

45) [pic]

46) [pic]

47) [pic]

48) Convert to exponential equation [pic]

49) Find the equation of the line (in slope-intercept form) that passes through (3,-1) and (2,-3).

50) Find the distance between the points (7,-5) and (8,-2)

51) Is the equation [pic] a function?

52) Write an equation of a line that is not a function.

Let [pic]Answer questions 50-54

53) Use the leading coefficient test to determine the graph’s end behavior

54) Find the x-intercepts. State whether the graph crosses or touches and turns around the x-axis.

55) Find the y-intercept

56) Determine whether the graph has y-axis symmetry, origin symmetry or neither

57) What are the maximum number of turning points?

58)

Let [pic]. Find the following:

59) [pic]

60) [pic]

61) [pic]

62)

Solve the following inequalities. Write the solutions in interval notation:

63) [pic]

64) [pic]

65) [pic]

66) [pic]

67) [pic]

68) [pic]

69) [pic]

70) [pic] or [pic]

71) [pic] or [pic]

72) For the function [pic]

a) Find the vertex

b) Find the line of symmetry

c) Give the x, y coordinates of the maximum or minimum point

d) Give the range of the function

Given the following cost and revenue functions, find the profit function and find the maximum profit as well as the number of units needed to obtain the maximum profit.

73) Sales of Packard Bell computers have grown exponentially. The total revenue function, in millions, is given by [pic]where t is the number of years since 1990. Find Packard Bell’s revenues in 1999, 2002, and 2005 assuming the growth rate remains the same. When will its sales revenue to $10 million?

74) A company finds that its costs follow the function [pic] where x is the number of items made. How many items should it make to minimize its costs?

75) The sum of the width and length of a parallelogram is 90 cm. Find the dimensions for which the area is a maximum.

76) You have 80 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

Find all asymptotes: vertical, horizontal, and slant asymptotes of the functions.

77) [pic]

78) [pic]

79) Use your calculator to graph [pic]

a) What is the y-intercept, if any?

b) What is the x-intercept, if any?

c) What is (are) the vertical asymptote(s), if any?

d) What is the horizontal asymptote, if any?

80) Find the center and the radius of the circle [pic].

81) What is the domain of [pic]

82) What is the domain of [pic]

83) What is the domain of [pic]where [pic]

84) What is the domain of [pic] where [pic]

85) If the function [pic] is expressed as a composition of two functions f and g, find f and g so that [pic]

86) If the function [pic] is expressed as a composition of two functions f and g, find f and g so that [pic]

87) Find the equation of the line (in slope-intercept form) that passes through (5,-4) and is parallel to[pic].

88) Find the equation of the line passing through the point (-1,2) and perpendicular to the line [pic]

Given [pic]. Find the following:

89) [pic]

90) [pic]

91) [pic]

92) [pic]

93) Given [pic] and [pic]. Find the following:

a) [pic]

b) [pic]

c) [pic]

d) [pic]

94) Find the inverse of [pic]

95) Find the inverse of [pic]

Given [pic]

96) Is -2 a zero of [pic]?

97) Factor completely

98) Find all the zeros of [pic]

Given [pic]

99) Is 2 a zero of [pic]?

100) Factor completely

101) Find all the zeros of [pic]

102) Find a polynomial , [pic], of lowest degree with real coefficients and zeros [pic] and 4

103) Find a polynomial, [pic], of lowest degree with real coefficients and zeros [pic] and 2

104) Use synthetic division to determine whether 3 is a zero of[pic].

105) Find all the zeros of [pic]

106) Find all zeros of [pic].

Graph the following. State the domain, range, relative extrema, and intervals of increasing/decreasing.

107) [pic]

108) Write the equation of the function which has the same shape as [pic]but has been shifted 7 units to the right and then reflected about the x axis and up 5 units

109) Write the equation of the function which has the same shape as [pic]but has been shifted right 2 units and moved up 1 unit.

110) Use your calculator to graph [pic]. What is the domain? What is the range?

111) Suppose $2,000 is invested at [pic]percent, compounded continuously, and grows to $2,983.65 in 7 years. a) What is k? b) How much will be in the account after 9 years? c) How long does it take the money to double?

112) A piece of charcoal is found to contain 30% of its carbon-14. If the decay rate of carbon-14 is -0.00012, how old is the piece of charcoal?

113) The volume V of a given mass of a gas varies directly as the temperature T and inversely as the pressure P. If V=231 cubic centimeters when T = 42º and P=20 kg/square centimeters, what is the volume when T=30º and P=15 kg/square centimeters?

114) Y varies jointly as m and the square of n and inversely as p. [pic]when [pic]and [pic]. Find y when [pic]and [pic]

Use the given table to answer questions 113 – 115

for a given rational function [pic]where [pic].

[pic]

115) a) List the x-intercepts, if any, of [pic]. Write as an ordered pair.

b) List any y-intercepts, if any, of [pic]. Write as an ordered pair.

116) Find the following:

a) [pic]

b) [pic]

117) Are there any restrictions for [pic] If so, what are they? Explain.

Use the following graph for problems 116-119

[pic]

118) Find x such that [pic]

119) Find [pic]

120) Find [pic]

121) Find x such that [pic]

COLLEGE ALGEBRA REVIEW ANSWERS

1. 24

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

1. [pic]

7. [pic]

8. [pic]

9. [pic]

10. [pic]

11. [pic]

12. a) [pic]

b) [pic]

13. [pic]

14. 10

15. [pic]

16. [pic]

17. [pic]

18. [pic]

19. [pic]

20. [pic]

21. [pic]

22. [pic]

23. [pic]

24. [pic]

25. [pic]

26. [pic]

27. [pic]

28. [pic]

29. [pic]

30. [pic]

31. [pic]

32. [pic]

33. [pic]

34. 5713

35. [pic]

36. [pic]

37. i

38. Undefined

39. 0

40. 0.827

41. 1.611

42. 45.254

43. 4.644

44. [pic]

45. [pic]

46. 1.404

47. [pic]

48. [pic]

49. [pic]

50. Yes

51. [pic], or any vertical line

52. Falls both to the left and right

53. [pic]

54. The y intercept is 0

55. Neither

56. 3

57. 31

58. [pic]

59. [pic]

60. [pic]

61. [pic]

62. [pic]

63. [pic]or [pic]

64. [pic]

65. [pic][pic][pic]

66. [pic]

67. [pic]

68. [pic]

69. a) [pic] b) [pic] c) [pic] d) [pic]

70. 1999 $12.16 Million; 2002 $34.817 Million; 2005 $99.691 Million; 10 Million sometime in 1998

71. [pic]items

72. 45 cm. by 45 cm.

73. 20 yards by 20 yards, 400 yards squared

74. V.A.: [pic]; H.A.: [pic]

75. V.A.: [pic]; H.A.: [pic]

76. a) [pic] b)none c) [pic] d) as[pic]

77. [pic]

78. [pic]

79. [pic]

80. [pic]

81. [pic]

82. [pic]

83. [pic]

84. [pic]

85. [pic]

86. [pic]

87. [pic]

88. [pic]

89. [pic]

90. a) [pic] b) [pic] c) undefined d) -125

91. [pic][pic]

92. [pic]

93. Yes

94. [pic]

95. [pic]

96. Yes

97. [pic]

98. -1, -2 and 2

99. [pic]

100. [pic]

101. not a zero

102. [pic]

103. [pic]

104. [pic]; [pic]; rel. max. of 6.5 @ [pic]; rel. min. of 0.2937 @ [pic]; inc.: [pic]; dec.: [pic]

105. [pic]

106. [pic]

107. Domain:[pic]; range: [pic]

108. a) [pic] b)[pic] c) [pic] yr

109. 10,033 years old

110. 220 cm[pic]

111. 125

112. a) There are no x-intercepts in the table (where [pic]). If this was a polynomial function, then the Intermediate Value Theorem says there’s a zero between 1 and 2 (but this is a rational function); b) [pic]

113. a) [pic]; b) 3

114. At [pic], there is an error for y. This means that 4 is not in the domain of [pic]

115. [pic]

116. [pic]

117. [pic]

118. [pic]

119.

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