Math 0303 Departmental Final Exam Review May 2102


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Solve the linear inequality and graph the solution set. State the solution using interval notation.
1)  5x > - 20

2.4-21
 
A) (-∞, -4)
 
 
B) (-4, )
 
 
C) (4, )

 
 
D) (-∞, 4)
 

2) 
2.4-43
 
A) [10, )
 
B) [-2, )
 
C) (-∞, -2]
 
D) (-∞, 10]

Solve the linear inequality and state the solution set using interval notation, if applicable.
3) 
2.4-42
  A)  [-4, )
  B)  (-∞, 5]
  C) 
  D) 

Solve the double inequality for x. State the solution using interval notation.
4) 

2.5-55
  A)  [4, 6]
  B)  (-6, -4)
  C)  [-6, -4]
  D)  (4, 6)

5) 
2.5-59
  A)  (3, 7]
  B)  [3, 7]
  C)  (-7, -3]
  D)  [-7, -3)

Solve the absolute value equation and write the solution set using set notation.
6)  |r - 2| = 5
2.6-25
  A)  {-7}
  B)  {-3, 7}
  C)  { }
  D)  {3, 7}

7)  |x + 6| - 3 = 14

2.6-27
  A)  {-11, 11}
  B)  {17, 11}
  C)  {-5, 11}
  D)  {-23, 11}

Solve the absolute value equation involving two absolute values. Write the solution using set notation.
8)  |9x - 4| = |x - 7|
2.6-47
  A) 
  B) 
  C) 
  D)  { }

Solve the absolute value inequality. Graph the solution set, then write the answer using interval notation.
9)  |x + 9| < 15
2.6-55
  A)  (-∞, -24)
  B)  (-24, 6)
  C)  (-6, 24)
  D)  (-∞, 6)

Solve the absolute value equation or inequality. State the solution using set notation or interval notation, whichever is appropriate.
10)  |x + 6| > 16

2.6-73
  A)  (-10, 22)
  B)  (-22, 10)
  C)  (10, )
  D)  (-∞, -22) (10, )

Graph the solutions to the linear equation by plotting points.
11)  y = 2x - 2
3.1-51
  A) 
  B) 
  C) 
  D) 

Use the intercept method to graph the solutions of the linear equation.
12)  2x - 3y = 6


3.2-9

  A) 
  B) 
  C) 
  D) 

13)  y = - 3

3.2-35
  A) 
  B) 
  C) 
  D) 

14)  x = 4

3.2-29
  A) 
  B) 
  C) 
  D) 

Find the slope of the straight line through the two solution points.
15)  (8, 3) and (-4, 4)

3.3-31
  A)  m = -
  B)  m = -
  C)  m = - 12
  D)  m = -

16)  (-3, -9) and (-3, -1)

3.3-35
  A)  m = -
  B)  m = -
  C)  undefined
  D)  m = 8

 

17)  (-8, 8) and (1, 8)


3.3-33

  A)  m = 1
  B)  m = 2
  C)  m = 0
  D)  m = 11

Find the slope and the y-intercept by using the slope-intercept form of the equation of the line. If necessary, solve for y first.
18)  y = 4x - 5

3.3-51
  A)  m = -5, (0, 4)
  B)  m = 4, (0, 5)
  C)  m = 5, (0, 4)
  D)  m = 4, (0, -5)

Write the equation of the line having the given slope and passing through the given point.
19)  m = 3, (-3, 6)


3.4-23

  A)  x = 3y + 15
  B)  y = 3x + 15
  C)  y = 3x - 15
  D)  x = 3y - 15

Write the equation of the line passing through the given points.
20)  (-3, -4) and (-2, -6)


3.4-29

  A)  y = -10x - 2
  B)  y = -10x + 2
  C)  y = -2x - 10
  D)  y = 2x - 10

Determine if the pair of lines is parallel, perpendicular, or neither.
21)  y = 6x - 8
y
= - x - 1


3.4-33

  A)  perpendicular
  B)  parallel
  C)  neither

22)  y = 9x - 6
y
= 9x + 4


3.4-35

  A)  perpendicular
  B)  neither
  C)  parallel

23)  y = 5x - 4
y
= -5x - 8


3.4-39

  A)  perpendicular
  B)  neither
  C)  parallel

Write the equation of the line with the given conditions. If the line is not horizontal or vertical, write the equation in standard form, Ax + By = C.
24)  Perpendicular to the line given by y = 5x + 1
containing the point (0, -3).


3.4-48

  A)  5x + y = 5
  B)  5x + y = -15
  C)  x + 5y = -15
  D)  x - 5y = -15

25)  Parallel to the line given by y = - x - 1
containing the point (0, 1).


3.4-51

  A)  4x - 5y = 5
  B)  4x + 5y = 1
  C)  5x + 4y = 5
  D)  4x + 5y = 5

Graph the linear inequality in two variables on the coordinate plane.
26) 


3.5-7

  A) 
  B) 
  C) 
  D) 

Determine whether the relation represents a function.
27)  {(-4, -8), (-3, -4), (3, -1), (5, -8)}


3.6-17

  A)  function
  B)  not a function

Graph the linear function. State the domain and range of the function using interval notation.
28)  h(x) = - 3x - 5


3.6-29

  A)  D = (-∞, ); R = (-∞, )
  B)  D = (-∞, ); R = (-∞, )
  C)  D = (-∞, ); R = (-∞, )
  D)  D = (-∞, ); R = (-∞, )

29)  f(x) = x + 3


3.6-34

  A)  D = (-∞, ); R = (-∞, )
  B)  D = (-∞, ); R = (-∞, )
  C)  D = (-∞, ); R = (-∞, )
  D)  D = (-∞, ); R = (-∞, )

Evaluate the function at the given value of the independent variable. State the answer as an ordered pair.
30)  g(x) = 3x; g(-3)


3.6-37

  A)  (3, -9)
  B)  (-3, 0)
  C)  (-3, 9)
  D)  (-3, -9)

31)  f(x) = -3x; f(n)


3.6-41

  A)  (n, -3n)
  B)  (-3n, n)
  C)  (n, -3xn)
  D)  (n, 3n)

32)  g(x) = 8x + 3, g(a)


3.6-41

  A)  (a, 8a + 3)
  B)  (a, 24a)
  C)  (a, 11a)
  D)  (a, 11)

33)  f(x) = 5x2 + 4x + 2; f(-4)


3.6-46

  A)  (-4, 2)
  B)  (-4, 62)
  C)  (-4, 66)
  D)  (-4, 98)

34)  h(x) = 3x2 + 4x + 5; h(k)


3.6-46

  A)  (k, 3k2 + 4k + 5)
  B)  (k, 9k2 + 16k + 25)
  C)  (k, 3k2 + 16k + 5)
  D)  (k, 3k2 + 4k + 25)

35) 


3.6-49

  A)  (6, -4)
  B)  (6, 10)
  C)  (6, 6)
  D)  (6, -10)

36) 


3.6-49

  A)  (-9, -9)
  B)  (-9, 7)
  C)  (-9, 16)
  D)  (-9, -16)

37)  h(x) = ; h(-4)


3.6-46

  A)  (-3, -4)
  B)  (-4, -5)
  C)  (-4, -3)
  D)  (-4, 3)

Solve the system of linear equations using the Graphing Method. State the solution as an ordered pair, if possible. Otherwise, state "infinitely many solutions" or "no solution."
38) 


4.1-23

  A)  infinitely many solutions
  B)  {(3, -1)}
  C)  no solution
  D)  {(3, 1)}

Solve the system of linear equations using the Substitution Method.
39) 


4.2-9

  A)  { }
  B)  {(x, y)}
  C)  {(3, 7)}
  D)  {(17, -7)}

40) 


42.-13

  A)  { }
  B)  {(1, -1)}
  C)  {(x, y)}
  D)  {(-1, 2)}

Solve the system of linear equations using the Elimination Method.
41) 


4.3-7

  A)  {(-6, -13)}
  B)  {(6, -1)}
  C)  {(x, y)}
  D)  { }

42) 


4.3-13

  A)  {(x, y)}
  B)  {(5, -4)}
  C)  {(-1, 4)}
  D)  { }

Solve the equation.
43)  + = -


7.5-18

  A)  {-13}
  B)  {13}
  C)  {-14}
  D)  { }

44)  - =


7.5-31

  A)  {}
  B)  {24}
  C)  {-8}
  D)  {8}

Simplify using the product rule for radicals.
45) 


8.1-27

  A)  5
  B)  13
  C)  30
  D)  6

Write in simplified radical form. Assume that all variables represent positive real numbers.
46) 


8.1-81

  A)  13x3z4
  B)  6.5x3yz4
  C)  6.5x3z4
  D)  13x4z7

Perform the indicated operations. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.
47) 


8.1-99

  A) 
  B)  
  C) 
  D) 

Multiply. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.
48) 


8.2-19

  A)  2x4
  B)  3x2
  C)  6x2
  D)  3x4

Rationalize the denominator. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.
49) 


8.2-82

  A) 
  B)  -
  C) 
  D) 

50) 


8.2-85

  A) 
  B) 
  C) 
  D) 

Solve and write the solution using set notation.
51) 


8.3-9

  A)  {36}
  B)  {12}
  C)  {6}
  D)  {9}

52) 


8.3-34

  A)  { }
  B)  {-2}
  C)  {3}
  D)  {-2, 3}

Using the distance formula, find the distance between the points.
53)  (5, -2) and (2, 2)


8.4-13

  A)  25
  B)  6
  C)  5
  D)  10

54)  (10, 0) and (0, -11)


8.4-17

  A)  221
  B) 
  C)  21
  D) 

Find the principal nth root.
55) 


8.5-9

  A)  100
  B)  ±10
  C)  10
  D)  32

Simplify using the product rule or quotient rule for radicals. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.
56) 


8.5-7

  A)  
  B) 
  C) 
  D) 

Perform the indicated operations. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.
57) 


8.5-31

  A) 
  B) 
  C) 
  D)   

Solve and write the solution using set notation.
58) 


8.6-25

  A)  {13}
  B)  {64}
  C)  {1}
  D)  {61}

Determine whether the relation represents a function. If the relation is a function, state the domain and range.
59)  {(1, 9), (-1, -8), (-6, -5), (6, -8)}


9.1-7

  A)  Yes, D = {-8, -5, 9}; R = {-6, -1, 1, 6}
  B)  No
  C)  Yes, D = {-6, -1, 1, 6}; R = {-8, -8, -5, 9}
  D)  Yes, D = {-6, -1, 1, 6}; R = {-8, -5, 9}

60)  {(2, 9), (-2, -9), (-2, -4), (6, -9)}


9.1-9

  A)  Yes, D = {-9, -4, 9}; R = {-2, 2, 6}
  B)  No
  C)  Yes, D = {-2, -2, 2, 6}; R = {-9, -9, -4, 9}
  D)  Yes, D = {-2, 2, 6}; R = {-9, -4, 9}

Find the functional value and write the answer as an ordered pair.
61)  f(x) = 9x + 4, f(-3)


9.1-11

  A)  (-3, 31)
  B)  (-3, -31)
  C)  (-3, -23)
  D)  (-3, 23)

62)  h(x) = 3x2 - 7x - 4, h(-5)


9.1-19

  A)  (-5, 106)
  B)  (-5, -114)
  C)  (-5, 36)
  D)  (-5, -44)

63) 


9.1-21

  A)  (-3, -19)
  B)  (-3, -11)
  C)  (-3, 11)
  D)  (-3, 19)

Find the functional value.
64)  g(x) = -x2 - 4x + 9; g(t)


9.1-29

  A)  -t2 - 4x + 9
  B)  -t2 - 4t + 9t
  C)  -t2 + 4t + 9
  D)  -t2 - 4t + 9

65)  g(x) = 2x2 - 5x - 3, g(x - 1)


9.1-33

  A)  2x2 - 9x + 4
  B)  2x2 - 11x - 6
  C)  2x2 - 9x - 6
  D)  -9x2 + 2x + 4

66)  f(x) = x2 + 6, f(a + h)


9.1-43

  A)  a2 + 2ah + h2 + 6
  B)  a2 + h2 + 6a + 6h
  C)  a2 + h2 + 6
  D)  a2 + 2ah + h2 + 6a + 6h

67)  f(x) = 8x + 8,


9.1-39

  A)  8h
  B)  8a + 8h
  C)  16
  D)  8

68)  f(x) = 7x2,


9.1-43

  A)  49a + 7h
  B)  7a + 7h
  C)  14a + 7h
  D)  14a + 14h

Find the following function and its domain.
69)  Let f(x) = 4 - 9x and g(x) = -2x + 9. Find (f + g)(x).


9.2-9

  A)  2x, D = (-∞, )
  B)  -2x + 4, D =
  C)  -11x + 13, D = (-∞, )
  D)  -7x + 13, D =

70)  Let f(x) = 2x2 - 3 and g(x) = 7x - 4. Find (f - g)(x).


9.2-12

  A)  2x2 - 7x - 7, D = (-∞, )
  B)  9x + 1, D = { x 1}
  C)  2x2 - 7x + 1, D = (-∞, )
  D)  -5x - 7, D =

71)  Let f(x) = 5x + 1 and g(x) = 2x - 5. Find (x).


9.2-22

  A)  , D =
  B)  , D =
  C)  , D =
  D)  , D =

72)  Let f(x) = 5x2 - 2 and g(x) = 4x + 1. Find (f g)(x).


9.2-16

  A)  20x3 + 5x2 - 2, D = (-∞, )
  B)  20x3 - 8x - 2, D = { x 0}
  C)  20x3 + 5x2 - 8x - 2, D = (-∞, )
  D)  5x2 + 4x - 2, D = (-∞, )

Find the composition and its domain. Evaluate as indicated.
73)  Let f(x) = 7x + 15 , g(x) = 4x - 1. Find (f g)(a).


9.2-39

  A)  28a + 8, D = (-∞, )
  B)  28a + 59, D = (-∞, )
  C)  28a + 8, D =
  D)  28a + 59, D =

74)  Let f(x) = 4x2 + 3x + 8, g(x) = 3x - 5. Find (f g)(x).


9.2-43

  A)  12x2 + 9x + 19, D = (-∞, )
  B)  4x2 + 3x + 3, D = [0, )
  C)  4x2 + 9x + 19, D = (-∞, )
  D)  12x2 + 9x + 29, D = [0, )

75)  Let f(t) = , g(t) = 4t + 8. Find (f g)(t).


9.2-41

  A)  4 + 8, D = [5, )
  B)  4 + 8, D = (5, )
  C)  , D =
  D)  , D =

76)  Let f(x) = -2x + 2, g(x) = 3x2 + 2x + 7. Find (g f)(6).


9.2-43

  A)  287
  B)  -72
  C)  -43
  D)  -252

Graph the function by plotting points. State the domain and range.
77)  f(x) = 5


9.3-13

  A)  D = {5}
R = (-∞, )
  B)  D = {5}
R = (-∞, )
  C)  D = (-∞, )
R = {5}
  D)  D = (-∞, )
R = (-∞, )

78)  g(x) = x - 4


9.3-15

  A)  D = (-∞, )
R = (-∞, )
  B)  D = (-∞, )
R = [-4, )
  C)  D = (-∞, )
R = [-4, )
  D)  D = (-∞, )
R = (-∞, )

79)  h(x) = x2 - 2


9.3-29

  A)  D = (-∞, )
R = [0, )
  B)  D = (-∞, )
R = (-∞, )
  C)  D = (-∞, )
R = [-2, )
  D)  D = [-2, )
R = [0, )

80)  f(x) =


9.3-32

  A)  D = [-9, )
R = (-∞, )
  B)  D = (-∞, )
R = [0, )
  C)  D = (-∞, )
R = [-9, )
  D)  D = [-9, )
R = [0, )

Match the function with the appropriate graph of the transformation of the function
81)  f(x) = (x + 4)2 - 5


9.4-11

  A) 
  B) 
  C) 
  D) 

Using transformations and/or reflections and one of the basic graphs, state the transformation and/or reflection and sketch the function.
82)  g(x) = (x - 3)2


9.4-14

  A)  This is the graph of f(x) = x2 shifted
up
3 units.
  B)  This is the graph of f(x) = x2 shifted
to the right
3 units.

  C)  This is the graph of f(x) = x2 shifted
to the left
3 units.
  D)  This is the graph of f(x) = x2 shifted
down
3 units.

83)  f(x) =


9.4-19

  A)  This is the graph of f(x) = shifted
to the right
3 units.
  B)  This is the graph of f(x) = shifted
to the left
3 units.
  C)  This is the graph of f(x) = shifted
up
3 units.
  D)  This is the graph of f(x) = shifted
down
3 units.

84) 


9.4-29

  A)  This is the graph of f(x) = shifted
7 units to the left and then shifted
up 2 units.
  B)  This is the graph of f(x) = shifted
to the right
2 units and then shifted
down 7 units.
  C)  This is the graph of f(x) = shifted
7 units to the right and then shifted
up 2 units.

  D)  This is the graph of f(x) = shifted
to the left
2 units and then shifted
down 7 units.

85)  g(x) = - - 3


9.4-25

  A)  This is the graph of f(x) = shifted
left
3 units and then reflected about
the x
-axis.
  B)  This is the graph of f(x) = reflected
about the y
-axis and then shifted
down
3 units.
  C)  This is the graph of f(x) = reflected
about the x
-axis and then shifted
down
3 units.
  D)  This is the graph of f(x) = shifted
left
3 units and then reflected about
the y
-axis.

86)   


9.4-47

  A)  This is the graph of f(x) = shifted
to the left
4 units, reflected about the
x
-axis, and then shifted up 7 units.
  B)  This is the graph of f(x) = shifted
to the right
4 units, reflected about the
y
-axis, and then shifted up 7 units.
  C)  This is the graph of f(x) = shifted
to the left
4 units, reflected about the
y
-axis, and then shifted up 7 units.
  D)  This is the graph of f(x) = shifted
to the right
4 units, reflected about the
x
-axis, and then shifted up 7 units.

Perform the indicated operations and write the answer in the standard form
87)  (-6 - 7i) + (12 + 4i)


10.1-21

  A)  6 - 3i
  B)  12 + 3i
  C)  6 + 3i
  D)  12 - 3i

88)  (2 - 7i)(9 + 4i)


10.1-41

  A)  46 - 55i
  B)  -28i2 - 55i + 18
  C)  46 + 55i
  D)  -10 - 55i

89) 


10.1-55

  A)  - i
  B)  - i
  C)  - i
  D)  - - i

Solve using the Zero Factor Property.
90)  (x - 3)(8x - 3) = 0


10.2-9

  A) 
  B) 
  C) 
  D) 

91)  7x2 + 19x - 6 = 0


10.2-15

  A) 
  B) 
  C) 
  D) 

Solve using the Square Root Property.
92)  (x - 7)2 = 25


10.2-29

  A)  {32}
  B)  {2, -12}
  C)  {5, -5}
  D)  {12, 2}

Solve by completing the square.
93)  x2 + 12x + 20 = 0


10.2-53

  A)  {2, -1}
  B)  {30, -10}
  C)  {-2, -10}
  D)  {2, 10}

94)  x2 - 6x + 18 = 0


10.2-55

  A)  {3 - 9i, 3 + 9i}
  B)  {3 - 3i, 3 + 3i}
  C)  {0, 6}
  D)  {3 + 3i}

Solve using the Quadratic Formula.
95)  5x2 + 8x = 4


10.3-11

 
A) 
 
B) 
 
C) 
 
D) 

96)  4x2 - 3x + 1 = 0


10.3-17

  A) 
  B) 
  C) 
  D) 

Solve the nonlinear equation.
97)  x4 + 12x2 - 64 = 0


10.4-5

  A)  {-4, 4, -16i, 16i}
  B)  {-2, 2, -4, 4}
  C)  {-2, 2, -4i, 4i}
  D)  {-4, 4, -2i, 2i}

98)  (4x - 4)2 - 6(4x - 4) - 7 = 0


10.4-11

  A) 
  B) 
  C) 
  D) 

Solve. Graph the solution on the real number line and state the solution using interval notation.
99)  (x + 2)(x - 5) < 0


10.5-7

  A)  (5, )
  B)  (-∞, -2) (5, )
  C)  (-∞, -2)
  D)  (-2, 5)

100)  > 0


10.5-27

  A)  (-∞, -9) (2, )

  B)  (-∞, -9)

  C)  (-9, 2)

  D)  (2, )

 

Determine if the ordered pair is a solution to the equation.
101)  (2, 2)2x + y = 6

3.1-21
A)  yes
  B)  no

Rationalize the denominator. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.
102) 

8.2-83
A)  -
  B) 
  C) 
  D) 

Solve and write the solution using set notation.
103) 

8.6-21
A)  {22}
  B)  {11}
  C)  {7}
  D)  {-4037}

Solve the application using the Pythagorean theorem.
104)  A bird flies 41 meters in a straight line from the top of a vertical cliff to a point on the ground 20 meters from the base of the cliff. Find the height of the cliff. Round to the nearest hundredth of a meter.

10.3-79
A)  Approximately 45.62 meters
  B)  Approximately 39.55 meters
  C)  Approximately 35.79 meters
  D)  Approximately 21 meters

 

Multiply. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.
105) 

8.2-51
A)  -172
  B)  
  C)  180
  D)  

 

 

 

Math 0303 Departmental Final Exam Review May 2102 Solutions

1) B
2) D
3) C
4) A
5) A
6) B
7) D
8) A
9) B
10) D
11) A
12) A
13) A
14) C
15) B
16) C
17) C
18) D
19) B
20) C
21) A
22) C
23) B
24) C
25) D
26) C
27) A
28) A
29) B
30) D
31) A
32) A
33) C
34) A
35) B
36) C
37) C
38) D
39) D
40) A
41) B
42) C
43) A
44) C
45) D
46) A
47) A
48) B
49) C
50) C
51) C
52) C
62) A
63) D
64) D
65) A
66) A
67) D
68) C
69) C
70) C
71) B
72) C
73) A
74) A
75) C
76) A
77) C
78) D
53) C
54) B
55) C
56) D
57) C
58) D
59) D
60) B
61) C
79) C
80) B
81) B
82) B
83) B
84) D

85) C
86) D
87) A
88) A
89) D
90) B
91) A
92) D
93) C
94) B
95) D
96) D
97) C
98) D
99) D
100) A
101) A
102) C
103) B
104) C
105) A

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