Math 112 Final Exam PRACTICE TEST
For the pair of functions, find the indicated sum, difference,
product, or quotient.
1) Find (f - g)(-1) when f(x) = -3x2 + 6
and g(x) = x + 5.
A) -1
B) 9
C) -3
Find the zero of f.
7) f(x) = 3x + 6
A) -2
D) -2
2) The population of a particular country was 21
million in 1983; in 1990, it was 25 million. The
exponential growth function A =21ekt describes
A) 3
C)
the population of this country t years after 1983.
Use the fact that 7 years after 1983 the population
increased by 4 million to find k to three decimal
places.
A) 0.895
B) 0.025
C) 0.035
D) 0.198
B) -3
1
256
A)
3) An initial investment of $480 is appreciated for 9
years in an account that earns 13% interest,
compounded quarterly. Find the amount of money
in the account at the end of the period. Use the
r nt
formula A = P(1+ ) or A=Pert
n
D)
1
16
B)
C)
D)
10) P(x) = -3x4 - x3 + x2 - 4x + 3
A)
B)
C)
D)
Find the requested function value.
11) Find (g(f(4)) when f(x) = -4x + 5 and
g(x) = 7x2 - 8x - 1.
B) $1441.94
D) $1470.26
A) -311
C) 25
Solve the problem.
4) Find out how long it takes a $2800 investment to
double if it is invested at 8% compounded
semiannually. Round to the nearest tenth of a year.
r nt
Use the formula A = P 1 +
.
n
B) 10
D) 934
12) Find (g (f(-2)) when f(x) =
x-2
and
2
g(x) = 2x + 1.
A) 6
B) 8.8 years
D) 9.2 years
B) -6
C) -
5
2
D) -3
Write the standard form of the equation of the circle with the
given center and radius.
13) (0, -7); 9
A) (x + 7)2 + y2 = 81
B) (x - 7)2 + y2 = 81
Solve the system.
5) x2 + y2 = 25
x -y =1
A) (3, -4), (4, -3)
C) (-3, -4), (4, 3)
D) -6
Find the correct end behavior diagram for the given
polynomial function.
9) P(x) = 5x3 + 6x2 - 7x + 7
Solve.
A) 8.6 years
C) 9 years
C) 2
Solve the equation.
1
8) log4
=x
64
Solve.
A) $1038.04
C) $1518.04
B) 6
C) x2 + (y + 7)2 = 81
D) x2 + (y - 7)2 = 9
Find the center and the radius of the circle.
14) x2 + y2 - 14x + 16y = -88
B) (-3, 4), (-4, 3)
D) (3, 4), (4, 3)
A) (-7, 8); r = 25
C) (7, -8); r = 5
State the domain of the rational function.
3x - 4
6) f(x) =
2x + 12
B) (8, -7); r = 25
D) (-8, 7); r = 5
Solve the polynomial inequality.
15) x2 - 10x + 21 > 0
A) (-∞, -6) ∪ (-6, ∞)
B) (-∞, ∞)
C) (-∞, -12) ∪ (-12, ∞)
D) (-∞, 6) ∪ (6, ∞)
A) (7, ∞)
C) (-∞, 3)
1
B) (3, 7)
D) (-∞, 3) ∪ (7, ∞)
Find the horizontal asymptote, if any, of the rational function.
x2 + 9x - 6
16) f(x) =
x-6
A) y = 1
C) y = 0
23)
f(x) =
x - 3, for x > 0
2, for x ≤ 0
A)
B) None
D) y = -9
6
y
4
8x3 - 3x - 7
17) f(x) =
5x3 - 2x + 8
A) y =
C) y =
2
3
2
B) None
8
5
D) y = 0
-6
-4
-2
2
4
6 x
2
4
6 x
2
4
6 x
2
4
6 x
-2
-4
-6
B)
Find the inverse of the one-to-one function.
18) f(x) = (x + 3)3
A) f-1 (x) =
C) f-1 (x) =
3
x+3
x-3
B) f-1 (x) =
D) f-1 (x) =
6
3
3
x - 27
4
x-3
2
-6
Solve the exponential equation.
19) 3 x = 18
-4
-2
-2
Give your answer as a decimal rounded to the
nearest thousandth.
A) 6.000
B) 2.631
C) 0.380
D) 1.792
-4
-6
C)
6
Find the zeros of the polynomial function and state the
multiplicity of each.
20) f(x) = -5x2 (x - 8)(x + 3)3
2
-6
-4
-2
-2
-4
-6
D)
6
Find the logarithm using the change-of-base formula.
21) log7 9.72
y
4
B) 0.8557
D) 0.9877
2
-6
Find the range of the given function.
22) f(x) = -3x2 - 12x - 17
A) [5, ∞)
C) (-∞, -5]
y
4
A) -3, multiplicity 3; 8, multiplicity 1
B) -3, multiplicity 3; 0, multiplicity 2; 8,
multiplicity 1
C) -3, multiplicity 3; 0, multiplicity 2; 3,
multiplicity 1; 8, multiplicity 1
D) -3, multiplicity 1; 3, multiplicity 1; 8,
multiplicity 1
A) 1.1687
C) 1.3886
y
-4
-2
-2
-4
B) [2, ∞)
D) (-∞, -2]
-6
Graph the function.
Use substitution to determine whether the given number is a
zero of the given polynomial.
24) -2; P(x) = x4 + 3x2 - 4
A) Yes
2
B) No
Solve the logarithmic equation.
25) log x = -4
6
1
A)
4096
C) 4096
Answer the question.
29) How can the graph of f(x) =
B) 1296
D)
obtained from the graph of y = x2 ?
1
1296
A) Shift it horizontally 11 units to the right.
Stretch it vertically by a factor of 2. Shift it 8
units up.
B) Shift it horizontally 11 units to the right.
1
Shrink it vertically by a factor of . Shift it 8
2
Find the domain and range of the function represented in the
graph.
26)
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
y
units down.
C) Shift it horizontally 11 units to the left.
1
Shrink it vertically by a factor of . Shift it 8
2
units down.
D) Shift it horizontally 11 units to the left.
Shrink it vertically by a factor of 2. Shift it 8
units down.
1 2 3 4 5 6 x
Give all possible rational zeros for the polynomial.
30) P(x) = -2x4 + 2x3 + 3x2 + 18
A) Domain: (-2, 1]; Range: [0, 3)
B) Domain: [-2, 1); Range: [-2, 5)
C) Domain: [-2, 1]; Range: [0, 3]
D) Domain: (-1, 2]; Range: [1, 3)
Find the requested value.
27)
2x + 1, if x < 1
f(8) for f(x) = 8x, if 8 ≤ x ≤ 12
8 - 2x, if x > 12
A) 64
B) -8
C) 3
1
(x + 11)2 - 8 be
2
A) ±1, ±2, ±1/2, ±1/3, ±1/6, ±1/9, ±1/18
B) ±1, ±1/2, ±2, ±3, ±6, ±9, ±18
C) ±1, ±1/2, ±2, ±3, ±3/2, ±6, ±9, ±9/2, ±18
D) ±1, ±2, ±3, ±6, ±9, ±18
Evaluate the function for the given values of a and b. Then use
the intermediate value theorem to determine which of the
statements below is true.
31) a = -2 and b = -1
D) 25
P(x) = 7x5 - 3x3 + 4x2 + 5
A) P(-2 ) and P(-1) have the same sign,
therefore the intermediate value theorem
cannot be used to determine whether P has a
real zero between -2 and -1.
B) P(-2 ) and P(-1) have the same sign,
therefore the function P has a real zero
between -2 and -1.
C) P(-2 ) and P(-1) have opposite signs,
therefore the function P has a real zero
between -2 and -1.
D) P(-2 ) and P(-1) have opposite signs,
therefore the function P does not have a real
zero between -2 and -1.
Find the requested polynomial.
28) Find a polynomial function of degree 3 with -1, 3,
4 as zeros.
A) f(x) = 3x3 + 6x2 + 5x - 12
B) f(x) = x3 + 8x2 + 5x - 3
C) f(x) = x3 - 6x2 + 5x + 12
D) f(x) = x3 + 6x2 + 5x - 12
Find the oblique asymptote, if any, of the rational function.
x2 - 6x + 7
32) f(x) =
x+6
A) x = y + 6
C) None
3
B) y = x + 13
D) y = x - 12
Find the inverse of the function.
1
33) f(x) = x + 3
8
39) 8x + 5y > -2
A)
10
A) f-1 (x) = 8x - 24
1
B) f-1 (x) = x + 8
3
C) f-1 (x) = 8x + 24
D) f-1 (x) =
1
x-3
8
-10
Find the vertical asymptote(s) of the graph of the given
function.
x+6
34) g(x) =
x-7
A) y = 7
C) x = -7
10
-10
B)
B) x = -6
D) x = 7
10
Determine whether the given function is one-to-one. If it is
one-to-one, find a formula for the inverse.
35) f(x) = 7x3 + 8
-10
3 x
-8
A) f-1 (x) =
7
C) f-1 (x) =
3 x-8
7
10
3 x+8
B) f-1 (x) =
7
-10
D) Not one-to-one
C)
10
Provide the requested response.
36) Suppose that a polynomial function of degree 4
with rational coefficients has -4, -3, -3 - i as zeros.
Find the other zero.
A) 3 + i
B) 3 - i
C) -3 - i
D) -3 + i
-10
Solve the system of equations using matrices. Use
Gauss-Jordan elimination.
37)
4x - y - 2z = -7
-4x + 8y + 5z = 46
8x - 3y + z = 13
A) {(2, 3, 6)}
B) {(-2, 3, 4)}
C) Infinite Solutions
D) No Solution
10
-10
D)
10
-10
Use Gaussian elimination to find the complete solution to the
system of equations, or state that none exists.
38) x + y + z = 7
x - y + 2z = 7
2x + 3z = 14
A) {(1, -5, 11)}
B) {(2,, 3, 2)}
C) No Solution
D) Infinite Solutions
10
-10
Determine whether there is a maximum or minimum value for
the given function, and find that value.
40) f(x) = x2 - 20x + 107
A) Maximum: -7
C) Maximum: 10
Match the inequality with a graph.
4
B) Minimum: 7
D) Minimum: 0
Determine the intervals on which the function is increasing,
decreasing, and constant.
41)
5
4
3
2
1
-5 -4 -3 -2 -1-1
-2
-3
-4
-5
Find the vertex of the parabola.
46) f(x) = 3x2 - 6x - 1
A) (1, -4)
C) (-4, 1)
y
47) 5 log m - log n
b
b
A) log (m 5 - n)
b
5m
B) log (
)
b n
1 2 3 4 5 x
C) log
m5
n
Use the compound interest formulas A = P 1 +
r nt
and
n
A = Pe rt to solve.
48) Find the accumulated value of an investment of
$6000 at 7% compounded continuously for 6
years.
A) $9231.77
B) $9004.38
C) $9131.77
D) $8520.00
Determine algebraically whether the function is even, odd, or
neither even nor odd.
42) f(x) = 9x4 + 6x - 7
B) Odd
b
D) log m 5 ÷ log n
b
b
A) Increasing on (-3, 1); Decreasing on (-5, -3)
and (0, 5); Constant on (1, 2)
B) Increasing on (-3, -1); Decreasing on (-5, -2)
and (2, 4); Constant on (-1, 2)
C) Increasing on (-5, -3) and (2, 5); Decreasing
on (-3, 0); Constant on (0, 2)
D) Increasing on (-3, 0); Decreasing on (-5, -3)
and (2, 5); Constant on (0, 2)
A) Neither
B) (-1, 4)
D) (4, -1)
Solve the rational inequality. Express the solution set in
interval notation.
-x + 9
49)
≥0
x-5
C) Even
Use synthetic division to find the quotient and the remainder.
43) (2x 5 - x4 + 3x2 - x + 5) ÷ (x - 1)
A) (-∞, 9]
C) (5, 9]
A) Q(x) = (2x4 + x3 + 4x2 + 3x); R(x) = 8
B) Q(x) = (2x4 + x3 - x2 + 2x + 1); R(x) = 6
B) (-∞, 5) or [9, ∞)
D) [5, 9]
Determine whether the graph is the graph of an even function,
an odd function, or a function that is neither.
50)
C) Q(x) = (2x4 - 3x3 - x); R(x) = 6
D) Q(x) = (2x4 + x3 + x2 + 4x + 3); R(x) = 8
y
10
Use properties of logarithms to expand the logarithmic
expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
x+2
44) log
3 x5
8
6
4
2
-10 -8 -6 -4 -2
-2
A) log (x + 2) - log x
3
3
B) log (x + 2) + 5 log x
3
3
C) 5 log x - log (x + 2)
3
3
D) log (x + 2) - 5 log x
3
3
4
6
8 10 x
-4
-6
-8
-10
A) Odd
The nth term of a sequence is given. Find the first 4 terms.
45) a n = 7n - 2
A) 9, 12, 19, 26
C) 5, 16, 19, 30
2
B) 5, 12, 19, 26
D) 7, 12, 19, 26
5
B) Neither
C) Even
51)
10
Graph the solution set of the system of inequalities or indicate
that the system has no solution.
54) x2 + y2 ≤ 49
y
8
7x + 5y ≤ 35
6
4
A)
2
-10 -8 -6 -4 -2
-2
2
4
6
10
8 10 x
y
-4
5
-6
-8
-10
A) Odd
B) Neither
-10
C) Even
-5
5
10
x
5
10
x
5
10
x
-5
52)
y
-10
8
B)
6
10
4
y
2
-10 -8 -6 -4 -2
-2
2
4
6
5
8 10 x
-4
-6
-10
-5
-8
-5
A) Odd
B) Neither
C) Even
-10
The graph of a quadratic function is given. Determine the
function's equation.
53)
C)
10
y
y
5
10
8
6
4
-10
-5
2
-10 -8 -6 -4 -2-2
2 4
6
8 10
-5
x
-4
-10
-6
-8
-10
Is this the graph of a function? Is its inverse a function?
55)
A) j(x) = -x2 + 3
B) g(x) = -x2 + 6x + 9
y
8
C) f(x) = -x2 - 6x - 9
D) h(x) = -x2 - 3
6
4
2
-10 -8 -6 -4 -2-2
2
4 6
8 10
x
-4
-6
-8
-10
A) yes, no
C) no, no
6
B) no, yes
D) yes, no
Answer Key
Testname: 112MC-LEXAMPRACTTESTSU13
1) A
2) B
3) C
4) B
5) C
6) A
7) A
8) B
9) C
10) A
11) D
12) D
13) C
14) C
15) D
16) B
17) C
18) D
19) B
20) B
21) A
22) C
23) C
24) B
25) D
26) A
27) A
28) C
29) C
30) C
31) C
32) D
33) A
34) D
35) C
36) D
37) A
38) D
39) C
40) B
41) D
42) A
43) D
44) D
45) B
46) A
47) C
48) C
49) C
50) C
51) C
52) A
53) D
54) B
55) A
7