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MTH 112 Final Exam
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Turn in all scratch work paper with the test.
1.
2.
3.
4.
Choose the equation shown in the graph.
A.
y= x − 3
B.
=
y x2 − 3
C.
y=
D.
=
y x3 − 3
x −3
E.
None of these
E.
None of these
E.
None of these
E.
None of these
Find the product and write in standard form: (7 + 9i )(3 − 8i )
A.
− 51+ 83i
B.
93 + 29i
C.
64i
D.
93 − 29i
Write
− 15
as a complex number in standard form.
2+i
15
− 15i
2
A.
− 6 + 3i
B.
−
C.
− 6 − 15i
D.
1
−6+ i
3
Solve the equation by factoring: 2 x 2 + 4 x = 9 x + 18
A.
9

2, − 
2

B.
9

− 2, 
2

C.
9 
 
2
D.
23 

18,

2

5.
6.
7.
8.
9.
Use the square root method to solve the equation: ( x − 2) 2 = 18
A.
{2 + 3 2 }
C.
{2 − 3
2, 2 + 3 2
}
B.
{5 −
D.
{− 16, 20}
2, 5 + 2
}
E.
None of these
Use the quadratic formula to solve the equation: x 2 + 3 x − 1 = 0
A.
{1,
− 2}
C.
 − 3 − 13 − 3 + 13 
,


2
2


B.
 − 1 − 13 − 1 + 13 
,


6
6


D.
− 3 − 5 − 3 + 5 
,


2 
 2
E.
None of these
Express the interval in set-builder notation: (− ∞, − 3]
A.
{ x | x < −3}
B.
{ x | x > −3}
C.
{ x | x ≥ −3}
D.
{ x | x ≤ −3}
E.
None of these
E.
None of these
E.
None of these
Solve the inequality: 4 x + 3 > 5 x − 9
A.
(12, ∞)
B.
(−12, ∞)
C.
(−∞, 12)
D.
(−∞, − 12)
Find f (−2) : f ( x) = x 3 + 2 x 2 − 3 x + 4
A.
14
B.
–6
C.
26
D.
10
10.
Determine which of the following two graphs represent the graph of a function:
Graph I
11.
12.
13.
Graph II
A.
Only graph I
B.
Only graph II
C.
Both graphs I and II
D.
Neither graph I nor II
E.
None of these
E.
None of these
Determine the interval on which the function is increasing.
A.
(− ∞, − 3)
B.
(1, 4)
C.
(3, ∞ )
D.
(− 3, 3)
Find the equation of a line with a slope of 4 and passing through the point (5, − 3) .
A.
y = 4 x + 17
B.
y = 4 x + 23
C.
y = 4 x − 17
D.
y = 4x − 3
E.
None of these
E.
None of these
Determine the domain of the function: f ( x) = x − 6
A.
(6, ∞)
B.
(−∞, 6)
C.
[6, ∞)
D.
(−∞, 6)  (6, ∞)
14.
15.
16.
17.
18.
19.
Find f − g for the given functions: f ( x) = 7 x + 9, g ( x) = 4 x − 1
A.
3 x 2 + 10 x
B.
3 x + 10
C.
3x + 8
D.
3x 2 + 8
E.
None of these
E.
None of these
E.
None of these
Find ( f  g )( x) for the given functions: f ( x) = 7 x + 9, g ( x) = 4 x − 1
A.
28 x + 2
B.
28 x + 35
C.
28 x + 8
D.
28 x + 16
Find the inverse function of f ( x ) = 3 x + 4 .
A.
f −1 ( x ) = 4 x + 3
B.
C.
x−4
f −1 ( x ) =
3
D.
x−3
f −1 ( x ) =
4
x
f −1 ( x ) = − 4
3
Divide the first polynomial by the second using long division: (9 x 3 − 6 x 2 − 8 x − 3) ÷ (3 x + 2)
A.
8
7
3x 2 − x −
3
3x + 2
C.
3 x 2 − 4 x − 16 +
23
3x + 2
B.
3x 2 − 4 x − 2 +
D.
3x 2 − 4 x −
7
3x + 2
3
3x + 2
E.
None of these
Divide the first polynomial by the second using synthetic division: (2 x 3 − 22 x − 40) ÷ ( x − 4)
A.
2 x 2 + 14 x −
96
x−4
B.
2 x 2 − 8 x + 10 −
C.
2 x 2 − 14 x −
96
x−4
D.
2 x 2 + 8 x + 10
80
x−4
E.
None of these
E.
None of these
Find all the zeros of the polynomial function: f ( x) = x 3 − 6 x 2 + 9 x − 4
A.
{− 1, 1, 4}
B.
{1, 4}
C.
{− 1, − 4}
D.
{− 4, − 1, 1}
20.
Which of the following is a graph of the function: f ( x) =
A.
B.
C.
D.
E.
21.
22.
x −1
x+2
None of these
Solve the inequality: x 2 + 13 x ≤ 0
A.
(−13, 0)
B.
(−∞, − 13]  [0, ∞)
C.
(−∞, − 13)  (0, ∞)
D.
[−13, 0]
Change the logarithmic expression to exponential form: log 2
2
A.
1
  = −3
8
C.
1
 
8
B.
(−3) 2 =
1
8
D.
(2) −3 =
1
8
−3
=2
E.
None of these
E.
None of these
1
= −3
8
23.
24.
25.
26.
27.
28.
Change the exponential expression to logarithmic form:
8=2
1
3
A.
log 8 2 =
1
3
B.
log 2 8 =
C.
log 8 3 =
1
3
D.
log 8 2 = −3
Evaluate the logarithmic expression: log 3
3
E.
None of these
E.
None of these
E.
None of these
E.
None of these
1
9
A.
3
B.
1
C.
1
2
D.
−2
Expand the logarithmic expression as much as possible: log
x2 y
A.
2(log x + log y − log z )
B.
z
2 log x + log y − 12 log z
C.
log(2 x + y − 12 z )
D.
2 log x − log y + 12 log z
Rewrite the expression as a single logarithm: 2 ln x + ln z − 4 ln y
A.
x2z
ln 4
y
B.
ln
2x
y4z
C.
ln
x2
y4z
D.
ln
2 xz
4y
Use the change-of-base formula to evaluate the logarithm and round to three decimal places: log 5 20
A.
1.861
B.
1.301
C.
0.700
D.
0.537
E.
None of these
E.
None of these
Solve the equation: 2 2 x +1 = 32
A.
3
B.
2
C.
–3
D.
–2
29.
30.
31.
32.
33.
Solve the equation: log 5 ( x + 1) = 2
A.
33
B.
31
C.
5
D.
24
E.
None of these
E.
None of these
E.
None of these
E.
None of these
E.
None of these
Solve the equation: log 2 x + log 2 ( x − 3) = 2
A.
–1, 4
B.
4
C.
1
D.
–4, 1
Solve the system of equations by the substitution method:
A.
∅
B.
{(2, 1)}
C.
{(0, − 1)}
D.
{( x, y ) | x=
Solve the system of equations by the addition method:
A.
∅
B.
{(− 2, 1)}
C.
10}
{( x, y ) | 4 x − 3 y =
D.
{(1, − 2)}
Solve the nonlinear system of equations:
x= y − 2
2x − 2 y =
−2
y − 2}
4x − 3 y =
10
2x + 3 y =
−4
x+ y =
7
y =x 2 − 10 x + 25
A.
{(6, 3)}
B.
{(−6, 13), (−3, 10)}
C.
{(6, 1), (3, 4)}
D.
{(−6, − 3)}
MTH 112 Final Exam Key
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B
D
A
B
C
C
D
C
D
B
D
E
C
B
A
C
D
D
B
B
D
D
A
D
B
A
A
B
D
B
A
D
C