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College Algebra MATH 107
Fall, 2017, V1.1
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]; Range [2, 4]
Domain [– 4, 2]; Range [2, 3]
Domain [– 4, 2]; Range [– 3, 3]
Domain [– 3, 3]; Range [– 4, 2]
2. Solve:
A.
B.
C.
D.
−7 − 4 x = x + 3
2. ______
−1/2
−8, −2
−2
No solution
Page 1 of 11
College Algebra MATH 107
Fall, 2017, V1.1
3. Determine the interval(s) on which the function is decreasing.
A.
(– 1, 3)
B.
(– 2, 2)
C.
(– ∞, –1) and (3, ∞)
D.
(– 2.5, 1) and (4.5, ∞)
4. Determine whether the graph of y = 3 x is symmetric with respect to the origin,
the x-axis, or the y-axis.
3. ______
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 − 4x ≤ 5 .
5. ______
(–∞, 1/2] ∪ [3, ∞)
(–∞, 1/2]
[1/2, ∞)
[1/2, 3]
Page 2 of 11
College Algebra MATH 107
Fall, 2017, V1.1
6. Which of the following represents the graph of 9x − 2y = 18 ?
A.
B.
C.
D.
6. ______
Page 3 of 11
College Algebra MATH 107
Fall, 2017, V1.1
7. Write a slope-intercept equation for a line parallel to the line x + 4y = 7 which passes through
the point (–12, 5).
7. ______
A.
y = −4 x − 43
B.
y=
C.
1
y = − x+5
4
D.
1
y = − x+2
4
1
x+8
4
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 but not one-to-one.
It is the graph of an absolute value relation.
It is not the graph of a function..
Page 4 of 11
College Algebra MATH 107
9. Express as an equivalent expression: 4 log x – log (y + 6) + log 1
A.
x4
log
y+6
B.
log(4 x)
log( y + 6)
C.
4x +1
log
y+6
D.
log ( 4 x − y − 5)
10. Which of the functions corresponds to the graph?
Fall, 2017, V1.1
9. ______
10. ______
A. f ( x ) = 2e− x
B. f ( x ) = e− x + 1
C. f ( x ) = e−2x
D. f ( x ) = 1 − e x
Page 5 of 11
College Algebra MATH 107
Fall, 2017, V1.1
11. Suppose that a function f has exactly two x-intercepts.
Which of the following statements MUST be true?
11. ______
A.
B.
C.
D.
f is a linear function.
f is a quadratic function.
f is an invertible function.
The equation f (x) = 0 has exactly two real-number solutions.
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 – 3) – 2
g(x) = f (x + 2) – 3
g(x) = f (x – 2) – 3
g(x) = f (x + 3) – 2
Page 6 of 11
College Algebra MATH 107
Fall, 2017, V1.1
SHORT ANSWER:
13. Multiply and simplify: (6 + i)(7 + 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+5
≤0.
x−7
Answer: ________
Answer: ________
15. Water initially at 190° F. is left in a room of temperature 70° F to cool.
– 0.096 t
After t minutes, the temperature T of the water is given by T(t) = 70 + 120e
Find the temperature of the water 25 minutes after it is left to cool. (Round to the nearest degree.)
Answer: ________
1
16. Find the value of the logarithm: log 2 .
16
17. Solve:
74−5 x = 49 .
Answer: ________
Answer: ________
18. Suppose $2,200 is invested in an account at an annual interest rate of 3.2% 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 + 37.
(a) Find the vertex.
Answer: ________
(b) State the range of the function.
Answer: ________
(c) On what interval is the function increasing?
Answer: ________
Page 7 of 11
College Algebra MATH 107
Fall, 2017, V1.1
20. Consider the polynomial P(x), shown in both standard form and factored form.
1
1
7
1
1
P ( x) = − x 4 − x3 + x 2 + x − 2 = − ( x + 3)( x + 1)( x − 1)( x − 2)
3
3
3
3
3
(a) Which sketch illustrates the end behavior of the polynomial function?
B.
A.
vvvv
C.
vvvv
D.
vvvv
vvvv
Answer: ________
(b) State the zeros of the function.
Answer: ________________
(c) State the y-intercept.
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) =
x
2
Fall, 2017, V1.1
.
x −4
(a) State the domain.
Answer: _________________
(b) State the horizontal asymptote.
Answer: _________________
(c) State the vertical asymptote(s).
Answer: _________________
(d) Which of the following represents the graph of f ( x) =
x
x2 − 4
GRAPH A.
GRAPH B.
GRAPH C.
GRAPH D.
?
Answer: ______________
Page 9 of 11
College Algebra MATH 107
Fall, 2017, V1.1
SHORT ANSWER, with work required to be shown, as indicated.
22. Let f ( x) =
x − 6 and g(x) = x – 9.
f
(a) Find (15) . Show work.
g
(b) Find the domain of the quotient function
f
. Explain.
g
23. Points (1, 2) and (–5, 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 y-axis.
24. Find the equation for a line which passes through the points (5, 1) and (9, –7). Write the
equation in slope-intercept form. Show work.
25. Lance, a resident of Metropolis, pays Metropolis an annual tax of $65 plus 1.4% of his
annual income. If Lance paid $863 in tax, what was Lance’s income? Show work.
2
26. Let f (x) = 4x + 9 and g(x) = x – 1.
(a) Find the composite function ( f o g )( x ) and simplify. Show work.
(b) Find ( f o g )( −2) . Show work.
2
27. Find the exact solutions and simplify as much as possible: 5x = 1 + 6x. Show work.
28. Given the function f ( x) =
1
x − 2 , find a formula for the inverse function. Show work.
9
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College Algebra MATH 107
Fall, 2017, V1.1
29. Donut Creations, Inc. has determined that when x donuts are made daily, the profit P (in
dollars) is given by
P(x) = –0.001 x2 + 3.2x – 1350
(a) What is the company’s profit if 900 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 + 12
70
+ 2
= 0 . Show work.
x + 5 x − 25
Page 11 of 11
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