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College Algebra MATH 107
Fall, 2017, V1.11
MATH 107 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #1–12 are Multiple Choice.
Problems #13–21 are Short Answer. (Work not required to be shown)
Problems #22–30 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function.
1. ______
4
2
-2
-4
2
4
-2
-4
A.
B.
C.
D.
Domain [1/2, 3/2]; Range [0, 1]
Domain [–1, 3]; Range [–3, 1]
Domain [–1, 1]; Range [–1, 1]
Domain [–3, 1]; Range [–1, 3]
2. Solve:
A.
B.
C.
D.
19 − 3 x = 3 − x
2. ______
No solution
8
−2
−2, 5
Page 1 of 11
College Algebra MATH 107
Fall, 2017, V1.11
3. Determine the interval(s) on which the function is decreasing.
A.
(–∞, – 4) and (1, ∞)
B.
(– 4, 1)
C.
(– 5.5, –2)
D.
(–∞, –2)
3. ______
4. Determine whether the graph of y = x − 5 is symmetric with respect to the origin,
the x-axis, or the y-axis.
4. ______
A.
symmetric with respect to the x-axis only
B.
symmetric with respect to the y-axis only
C. symmetric with respect to the origin only
D. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and
not symmetric with respect to the origin
5. Solve, and express the answer in interval notation:
A.
B.
C.
D.
7 − 3x ≤ 17 .
5. ______
(–∞, –10/3]
[–8, 10/3]
[–10/3, 8]
(–∞, –10/3] ∪ [8, ∞)
Page 2 of 11
College Algebra MATH 107
Fall, 2017, V1.11
6. Which of the following represents the graph of 9x − 4y = 36 ?
A.
B.
C.
D.
6. ______
Page 3 of 11
College Algebra MATH 107
Fall, 2017, V1.11
7. Write a slope-intercept equation for a line parallel to the line x + 7y = 8 which passes through
the point (–14, 6).
7. ______
A.
y = − 7 x − 92
B.
y=
C.
1
y = − x+6
7
D.
1
y = − x+4
7
1
x+8
7
8. Which of the following best describes the graph?
A.
B.
C.
D.
8. ______
It is the graph of a function and it is one-to-one.
It is the graph of a function and it is not one-to-one.
It is the graph of a parabola.
It is not the graph of a function.
Page 4 of 11
College Algebra MATH 107
9. Express as a single logarithm:
A.
log(a + 1 − 2b )
B.
 a + 1
log

 2b 
C.
 a 
log 2 
b 
D.
 ab 
log 
 2 
Fall, 2017, V1.11
log a + log 1 – 2 log b.
10. Which of the functions corresponds to the graph?
9. ______
10. ______
A. f ( x ) = −e x + 3
B. f ( x ) = e− x + 2
C. f ( x ) = e x + 2
D. f ( x ) = e x + 3
Page 5 of 11
College Algebra MATH 107
Fall, 2017, V1.11
11. Suppose that a function f has exactly one x-intercept.
Which of the following statements MUST be true?
A.
B.
C.
D.
11. ______
f is a linear function.
The equation f (x) = 0 has exactly one real-number solution.
f (x) ≥ 0 for all x in the domain of f.
f is an invertible function.
12. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the right. (No
formulas are given.) What is the relationship between g(x) and f (x)?
12. ______
-4
4
4
2
2
2
-2
4
-4
2
-2
-2
-2
-4
-4
y = f (x)
4
y = g(x)
A.
B.
C.
D.
g(x) = f (x – 1) – 2
g(x) = f (x + 1) – 1
g(x) = f (x + 2) + 2
g(x) = f (x + 1) – 2
Page 6 of 11
College Algebra MATH 107
Fall, 2017, V1.11
SHORT ANSWER:
13. Multiply and simplify: (7 + 2i)(5 – 8i).
Write the answer in the form a + bi, where a and b are real numbers.
14. Solve, and write the answer in interval notation:
x+4
≤ 0.
x −1
Answer: ________
Answer: ________
15. A can of soda at 76° F. is placed in a refrigerator that maintains a constant temperature of 34°
F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by
T(t) = 34 + 42 e
– 0.058 t
Find the temperature of the soda 20 minutes after it is placed in the refrigerator. (Round to the
nearest tenth of a degree.)
Answer: ________
1
16. Find the value of the logarithm: log 4   .
 16 
Answer: ________
17. Solve: 79 x+5 = 49 .
Answer: ________
18. Suppose $3,400 is invested in an account at an annual interest rate of 5.7% compounded
continuously. How long (to the nearest tenth of a year) will it take the investment to double in
size?
Answer: ________
2
19. Let f (x) = x + 10x + 32.
(a) Find the vertex.
Answer: ________
(b) State the range of the function.
Answer: ________
(c) On what interval is the function decreasing?
Answer: ________
Page 7 of 11
College Algebra MATH 107
Fall, 2017, V1.11
20. Consider the polynomial P(x), shown in both standard form and factored form.
1
3
19
1
P ( x) = x 4 − x 3 − 3 x 2 + x + 6 = ( x + 3)( x + 1)( x − 2)( x − 5)
5
5
5
5
(a) Which sketch illustrates the end behavior of the polynomial function?
A.
B.
vvvv
C.
vvvv
D.
vvvv
vvvv
Answer: ________
(b) State the y-intercept.
Answer: ________________
(c) State the zeros of the function.
Answer: ________________
Answer: ________
(d) State which graph below is the graph of P(x).
GRAPH
A
GRAPH
B
GRAPH
C
GRAPH
D
Page 8 of 11
College Algebra MATH 107
21. Let f ( x) =
Fall, 2017, V1.11
3x 2 − 3
.
x2 − 4
(a) State the domain.
Answer: _________________
(b) State the vertical asymptote(s).
Answer: _________________
(c) State the horizontal asymptote.
Answer: _________________
(d) Which of the following represents the graph of f ( x) =
3x 2 − 3
?
x2 − 4
GRAPH A.
GRAPH B.
GRAPH C.
GRAPH D.
Answer: ______________
Page 9 of 11
College Algebra MATH 107
Fall, 2017, V1.11
SHORT ANSWER, with work required to be shown, as indicated.
22. Let f ( x) =
x + 5 and g ( x) = x − 3 .
f 
(a) Find  (−1) . Show work.
g
(b) Find the domain of the quotient function
f
. Explain.
g
23. Points (5, 4) and (–3, 6) are endpoints of the diameter of a circle.
(a) What is the length of the diameter? Give the exact answer, simplified as much as possible.
Show work.
(b) What is the center point C of the circle?
(c) Given the point C you found in part (b), state the point symmetric to C about the x-axis.
24. Find the equation for a line which passes through the points (1, 8) and (3, –2). Write the
equation in slope-intercept form. Show work.
25. A salesperson earns a base salary of $1,960 per month and a commission of 6.8% on the
amount of sales. If the salesperson has a paycheck of $4,197.20 for one month, what was the
amount of sales for the month? Show work.
26. Let f (x) = 5×2 + 9 and g(x) = x – 2.
(a) Find the composite function ( f o g )( x ) and simplify. Show work.
(b) Find ( f o g )( −1) . Show work.
2
27. Find the exact solutions and simplify as much as possible: 3x − 2 = 6x. Show work.
28. Given the function f ( x) =
1
x − 8 , find a formula for the inverse function. Show work.
4
Page 10 of 11
College Algebra MATH 107
Fall, 2017, V1.11
29. Donut Creations, Inc. has determined that when x donuts are made daily, the profit P, in
dollars, is given by
P(x) = –0.002 x2 + 4.7x – 1850
(a) What is the company’s profit if 800 donuts are made daily?
(b) How many donuts should be made daily in order to maximize the company’s profit? Show
work.
30. Solve:
x−6
16
+ 2
= 0 . Show work.
x − 4 x − 16
Page 11 of 11
Problems #1-12 are multiple choice. Record your choice for each problem.
Problems #13-21 are short answer. Record your answer for each problem.
Problems #22-30 are short answer with work required. When requested, show all work and write
all answers in the spaces allotted on the following pages. You may type your work using plaintext formatting or an equation editor, or you may hand-write your work and scan it. In either
case, show work neatly and correctly, following standard mathematical conventions. Each step
should follow clearly and completely from the previous step. If necessary, you may attach extra
pages.
MULTIPLE CHOICE. Record your answer choices.
1.
7.
2.
8.
3.
9.
4.
10.
5.
11.
6.
12.
SHORT ANSWER. Record your answers below.
13.
14.
15.
16.
17.
18.
19.
(a)
(b)
(c)
20.
(a)
(b)
(c)
(d)
21.
(a)
(b)
(c)
(d)
SHORT ANSWER with Work Shown. Record your answers and work.
Problem
Number
Solution
Answers:
(a)
(b)
Work/for part (a) and explanation for part (b):
22
Answers:
(a)
(b)
(c)
Work for part (a):
23
Answer:
Work:
24
Answer:
Work:
25
Answers:
(a)
(b)
Work for part (a) and for part (b):
26
Answer:
Work:
27
Answer:
Work:
28
Answers:
(a)
(b)
Work for (b):
29
Answer:
Work:
30
…
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