Algebra Final Exam Review

7/23/2019 Algebra Final Exam Review

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COLLEGE ALGEB RAFINAL EXAM REVIEW SHEET

Perform the indicated operation and give a simplified answer:

222

65 25 m -4 5m +17 m +6 7 3x x -9

1. -2. 3. x +4. x +3 x -1 5m -

2 6m 2 +18 mx 4x -12 15 x 7

Simplify the complex rational expressions:

3 1

+

3

y x

5.6.15 9x y

--

2

yyyx

Solve the equations:

7. 2(m -5) =m +1 8. x 2 -6x -


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11 =0 9. 3x 2 +2x =52332

10.3x -5x -1 =0 11. 3x =75 x 12. 12 x +16 x -28 x =013.x 4 -11 x 2 +28 =0 14. 3 19 x +1 -7 =-5 15. x +

2 +3 =x -12x 2 x 2 +10 -20 516. +=17. =x -1x -

3 x 2 -4x +3 x 2 -4 x +2

Solve the inequalities; write your answer using inequality notation:

3 p +4

18.3x +

7 =x -1 19. 4 >>-5-2

Given either the two points that lie on a line or the linear equation, find theslope:


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20.(3,-5) and (-5,7) 21. y =3x -7 22. -5x =-3023.6x -7 y =15 24. y =8 25. 3(x -5) +4 y =45 +4yFind the x and y intercepts:

26. 4x -3y =6 27. x =328. y =-1


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Find the equation of the line that passes through the given points, in slope-intercept form:

29. (30,1) and (3,10) 30. (1,6) and (1,-5) 31. (-1,-7) and (0,-17)32. (8,-2) and (0,-18)Find the equation of the line that passes through the given point, and is parallel to the line whoseequation is given:

33. 7x + 2y = 40; (6, 5) 34. -4x 5y = 20; (-5, 0) 35. y = 2x 4; (3, 4)Find the equation of the line that passes through the given point, and is perpendicular to the line whoseequation is given:

1

36. y = -3x 1; (-4, 2) 37. x 3y = 9; (2, 4) 38. y =x +9 ; (5, -5)6

Sketch the graph of the following lines by plotting the intercepts:

39. y = 2x + 1 40. 4x 3y = 12 41. x 2y = -2 42. 3x + 2y = 6Sketch the graph of the line with slope m that contains point P:

2

43. m =P(1, -4) 44. m = -5 P(-3, 2) 45. m = 0 P(0,3)3Find the following using k(x) =3x 2 -7 :

k(x +

h) -k(x)

46. k(2) 47. k(x +h) 48.h

Find the domain of the function, write your answers in interval notation:

4 -x

49. f (x) =3x 5 -7x +92 50. g(x) =x -7 51. h(x) =52. k(x) =x +6 -5x


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2xx +1 34x +7

53. m(x) =54. f (x) =x -5 55. y =

x 2 -25 6


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Given f(x)and g(x), find the value of the given combination function:

56. f (x) =x -3, g(x) =x +5;( f +g)( -2) 57. f (x) =-4x 2 -2, g(x) =x +7;( f -g)( -5).

f

..

58. f (x) =x -2, g(x) =-4x 2 +20 x +1;( fg )(3) 59. f (x) =4x -3, g(x) =2x 2 +14 x +3;

(-5)

g

Given f(x) and g(x), find the following composite function:

4 5

60. f (x) =3x +14, g(x) =5x -1;( f og)( x) 61. f (x) =, g(x) =;( f og)( x)x +


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3 6x

62. f (x) =4x +4, g(x) =2x 2 +5;(g of )( x) 63. f (x) =2x +4, g(x) =4x 2 +3;(g of )( x)Determine whether the two functions are inverses of each other:

x +7 2 +x 2 33

64. f (x) =7x -8, g(x) =65. f (x) =, g(x) =

66. f (x) =x -5, g(x) =x +5

8 x x -1

Find the inverse of each function:

5

x +2

67. h(x) =2x 5 +3 68. f (x) =69. g(x) =3 x +7 -4 70. k(x) =11 x -6 x +9

For the given quadratic functions, find the vertex and the x-and y-intercepts:

2 22

71. y = x +3 72. f (x) =4(x -1) -7 73. f (x) =-(x -


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5)74. f (x) =x 2 +6x -7 75. f (x) =x 2 -4x +3


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For #76-78, find the x and y intercepts of the polynomial function; write them as ordered pairs. Then,determine the correct graph of the function:

76. f (x) =x(2 -x)(4 -x)A. B. C. D.77. s(x) =x 3 +5x 2 +6x78. r(x) =x 2 -5x -6Use long division to find the quotient and remainder:

2x 3 -4x 2 +7x -3

79.x 2 +3


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Use synthetic division to find the quotient and remainder:

3 54

2x +5x -1 2x -3x +3x

80. 81.x +3 x -2

Use synthetic division to find all remaining zeros of f(x),given that c is a zero of f(x):

42 32

82. f (x) =x -

21 x -100;c =5 83. f (x) =x +2x -5x -6;c =284. f (x) =2x 3 -13 x 2 +10 x +25;c =

-1Given f(x),find the vertical asymptotes:

6 6x -5 4x 3 -x 2 +5x -1

85. f (x) =86. f (x) =87. f (x) =

x +4 10 -2x x 2 -2x -3

Given f(x),find the horizontal asymptotes:

6x -


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5 x x 2 -5x +13

88. f (x) =89. f (x) =290. r(x) =10 -2x x -9 x -2

Given f(x),find the slant asymptotes:

32 2

4x -x +5x -1 x -5x +13

91. f (x) =92. f (x) =x 2 -2x -3 x -2

Solve the polynomial inequalities; write your answer using interval notation.Show your work using a sign chart:

93. (x +1)( x -

3)( x -6) >0 94. x 2 (5 -x) =0 95. 2x 2 =15 x -27Solve the rational inequalities; write your answer using interval notation.Show your work using a sign chart:

x -7 10 4 3

96. =0 97. >5 98. =x +3 x x -1 x -5


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Solve the exponential equations:3x-5 x-2 7x 3x-5 x-2 7x

1

99. 8 =64 100. 100 =10

x x-1

101. 5 =26 102. 7 =13 (exact answer and four decimal places)3x-7

103. 2e =12 (exact answer and four decimal places)104. The population of a certain city is estimated to be increasing according tothe model0.012 tP(t) =300,000 e where t is the number of years from the present. Rounding to the neare

st person,what does the model predict that the population will be in 5 years?

Find the value of each logarithm without using a calculator:1

5 1

105. log 125 106. log 107. log 9 108. log5 23

16 1000

109. log 7 1 110. ln e 4Use the properties of logarithms to expand the expression. Simplify any log expressions that can beevaluated without the use of a calculator:

3 5

.

x pq

7 .

111. log10 x 112. ln.


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e

.7..x 2 y .

113. ln ..114. log125..+250.+125

3

.

.

Use the properties of logarithms to condense the expression as much as possible,writing the answer as asingle log term with a coefficient of 1 and a simplified argument.

115. log 5 x -2log 5 y 116. ln( x 2 y 5 ) -2ln x3

117. ln 3 +ln p -

6ln q 118. 5log (a b)+6log (a)-7log b119. log 7 (x 2 -9) -log 7 (x -3)


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Solve each logarithmic equation; give a decimal approximation when requested:

120. log 2 5x =4 121.log x 3log 2 = 2

122. log 4 8x =log 4 40 123.log(6x +4) =2

124. log 163x =7 125.log (4x +7)-log (x +1)=3

4

22

126.log 3 (x +1) +log 3 (x +3) =1 127. ln( x -2) +ln( x -5) =ln( x -1)

(round to 4 decimal places)

128. log 1 3x =2

3

Solve the system of equations:

7x -3y =26x +

5y =-1 9x -6 y =2

129.130. 131.

3y =13


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5x -2 y =-7 6x -4 y =5


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ANSWER KEY

1. .2. 6.3.4...

6.7. .=118. .=3259. .=-.

.,

.=1. .=..

11. .

=0,.=-5,.=512. .=0,.=

-..,.=113. .=-7,


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.=7,.=-2,.=214. =.. .=7

16. .=6,.=-217. No Solution18. $-4,

8.19. -4,2.. .=-..21. .=322. .=

undefined23. .=..24. .=0. .=undefined26. x-intercept:y-intercept:

-227. x-intercept: 3y-intercept: none28. x-intercept: noney-intercept: -129. .=-.


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.

.+11. .=131. .=-10.-1732. .=2.-1833. .=-...+

2634. .=-...-4. .=2.-

236. .=...+.37. .=-3.+10


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38. .=-6.+2539.40.41.


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42.43.44.


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45.46. 02.=547. 0.+1.=3..+6 .+31.-7232.

48. =6.+3.

49. -8,8.50. $7,8.51. -8,0..0,8.52. 5-8,..53. -8,

-5..-5,5..5,8.54. -8,8.55. -8,8.56. -257. -10458. 25

59.60. 15.+1161.7.

62. 32..


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+64.+3763. 16..+64.+6764. not inverses65. inverses66. inverses98.

67. 1. .=68. :. .=69. ;. .

=.+4.-770. 0. .=71. vertex: 0,3.x-intercepts: noney-intercept: 3

72. vertex: 1,-7.

.

.

x-intercepts: ,y-intercept: -3..


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73. vertex: 5,0.x-intercepts: 5y-intercept: -2574. vertex: -3,-16.x-intercepts: -7,1y-intercept: -775. vertex: 2,-1.x-intercepts: 1,3y-intercept: 376. x-intercepts: 0,2,4y-intercept: 0Graph: A77. x-intercepts: -3,-2,0y-intercept: 0

Graph: C78. x-intercepts: -1,6y-intercept: -6Graph: D79. Quotient: 2.-4Remainder: .+980. Quotient: 2..

-6.+23Remainder: -7081. Quotient: 2..+..+2..

+4.+11Remainder: 2282. .=-583. .=


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-3,.=-184. .=..,.=585. .=486. .=587. .=-1,.=3

88. .=-389. .=090. none91. .=4.+792. .

=.-393. -1,3..6,8.94. $5,8.95. =3,

#.96. -3,7.97. 0,2.98. 1,5..$17,


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8.99. .=1100. =-.101. .=?@.

[email protected]

102. .=?@[email protected]

?@..

103. .=?..2.9306

104. 318,551people105. 3


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106. -4107.108. -3109. 0110. 4111. 1+7log.112. ln.+ln.+5ln.-7113. 2ln

.+ln.-ln3114. 3+2log.+1.

115. log.5..116. ln-.117. ln5.118. log5K.119. log.+3.120. .

=.121. .=800122. .=5123. .=


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16124. .=..125. .=-..126. .=0127. .=4+56.2361128. .=-2129. 5.

.130. -1,1.131. No Solution


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Algebra Final Exam Review

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