COLLEGE ALGEBRA FINAL REVIEW
Similar problems can be found in Chapters P-4 of your textbook: College Algebra Essentials, 4thEdition by Blitzer.
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Solve.
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11)solve for L
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Write as a single logarithm and simplify,if possible.
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24)Write as the sum of difference of logarithms; express powers as factors.
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Simplify the following:
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Evaluate to 3 decimal places.
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Given: . Find the following to 3 decimal places.
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48)Convert to exponential equation
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 a function?
52)Write an equation of a line that is not a function.
Let 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?
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Let . Find thefollowing:
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Solve the following inequalities. Writethe solutions in interval notation:
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70)For the function
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 maximumprofit as well as the number of units needed toobtain the maximum profit.
71)Sales of Packard Bell computers have grown exponentially. The total revenue function, in millions, is given by 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?
72)A company finds that its costs follow the function where x is the number of items made. How many items should it make to minimize its costs?
73)The sum of the width and length of aparallelogram is 90 cm. Find the dimensionsfor which the area is a maximum.
74)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.
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77)Use your calculator to graph
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?
78)Find the center and the radius of thecircle .
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79)What is the domain of
80)What is the domain of
81)What is the domain of where
82)What is the domain of where
83)If the function is expressed as a composition of two functions f and g, find f and g so that
84)If the function is expressed as a composition of two functions f and g, find f and g so that
85)Find the equation of the line (in slope-intercept form) that passes through(5,-4) and isparallel to.
86)Find the equation of the line passing through the point (-1,2) and perpendicular to the line
Given . Find the following:
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91)Given and . Find the following:
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92)Find the inverse of
93)Find the inverse of
Given
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94)Is -2 a zero of ?
95)Factor completely
96)Find all the zeros of
Given
97)Is 2 a zero of ?
98)Factor completely
99)Find all the zeros of
100)Find a polynomial , , of lowest degree with real coefficients and zeros and 4
101)Find a polynomial, , of lowest degree with real coefficients and zeros and 2
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102)Use synthetic division to determine whether 3 is a zero of.
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103)Find all the zeros of
104)Find all zeros of .
Graph the following. State the domain,range, relative extrema, and intervals of increasing/decreasing.
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106)Write the equation of the function which has the same shape as but has been shifted 7 units to the right and then reflected about the x axis and up 5 units
107)Write the equation of the function which has the same shape as but has been shifted right 2 units and moved up 1 unit.
108)Use your calculator to graph . What is the domain? What is the range?
109)Suppose $2,000 is invested at 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?
110)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?
111)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 whenT = 42º and P=20 kg/square centimeters, what is the volume when T=30º and P=15 kg/square centimeters?
112)Y varies jointly as m and the square of n and inversely as p. when and . Find y when and
Use the given table to answer questions 113 – 115
for a given rational function where .
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113)a) List the x-intercepts, if any, of . Write as an ordered pair.
b) List any y-intercepts, if any, of . Writeas an ordered pair.
114)Find the following:
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115)Are there any restrictions for If so, what are they? Explain.
Use the following graph for problems 116-119
116)Find x such that
117)Find
118)Find
119)Find x such that
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COLLEGE ALGEBRA REVIEW ANSWERS
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1. 24
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13. a)
b)
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15. 10
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35. 5713
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38. i
39. Undefined
40. 0
41. 0.827
42. 1.611
43. 45.254
44. 4.644
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47. 1.404
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51. Yes
52. , or any vertical line
53. Falls both to the left and right
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55. The y intercept is 0
56. Neither
57. 3
58. 31
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64. and
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70. a) b) c) d)
71. 1999 $12.16 Million; 2002 $34.817 Million; 2005 $99.691 Million; 10 Million sometime in 1998
72. items
73. 45 cm. by 45 cm.
74. 20 yards by 20 yards, 400 yards squared
75. V.A.: ; H.A.:
76. V.A.: ; H.A.:
77. a) b)none c) d) as
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91. a) b) c) undefinedd) -125
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94. Yes
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97. Yes
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99. -1, -2 and 2
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102. not a zero
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105. ; ; rel. max. of 6.5 @ ; rel. min. of 0.2937 @ ; inc.: ; dec.:
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108. Domain:; range:
109. a) b) c) yr
110. 10,033 years old
111. 220 cm
112. 50
113. a) There are no x-intercepts in the table (where ). 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)
114. a) ; b) 3
115. At , there is an error for y. This means that 4 is not in the domain of
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