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College Algebra MATH 107
Fall, 2019, V1.24
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
-4
2
-2
4
-2
-4
A.
B.
C.
D.
Domain [–0.5, 1]; Range [0, 1]
Domain [–2,2]; Range (–, 1]
Domain [–3, 3]; Range [–3, 1]
Domain [–3, 1]; Range [–3, 3]
2. Solve:
A.
B.
C.
D.
−7 − 4 x = x + 3
2. ______
No solution
−8, −2
−2
−1/2
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College Algebra MATH 107
3. Determine the interval(s) on which the function is decreasing.
A.
( −,1) and ( 4,  )
B.
(1, 4 )
C.
( −1.25, 3.25 )
D.
( −,
Fall, 2019, V1.24
3. ______
− 1/ 3 ) and (3, 4.75)
4. Determine whether the graph of y = x − 9 is symmetric with respect to the origin,
the x-axis, or the y-axis.
4. ______
A.
symmetric with respect to the y-axis only
B.
symmetric with respect to the x-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: | 7 – 4x |  13.
A.
B.
C.
D.
5. ______
(–, –3/2]
(–, –3/2]  [5, )
(–, 5]  [–3/2, )
[–3/2, 5]
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College Algebra MATH 107
Fall, 2019, V1.24
6. Which of the following represents the graph of 7x − 3y = 21 ?
A.
B.
C.
D.
6. ______
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College Algebra MATH 107
Fall, 2019, V1.24
7. Write a slope-intercept equation for a line parallel to the line x – 4y = 6 which passes through
the point (–8, 3).
7. ______
A.
y = −4x − 29
B.
y=
1
x+3
4
C.
y=
1
x+5
4
D.
1
y = − x +1
4
8. Which of the following best describes the graph?
A.
B.
C.
D.
8. ______
It is the graph of a parabola.
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 not the graph of a function.
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College Algebra MATH 107
9. Express as an equivalent expression: 3 log (x + 4) – 2 log y + log 1
A.
 ( x + 4 )3 
log 

 y2 


B.
 x 3 + 64 
log 

2
 y

C.
12 log( x)
log(2 y )
D.
log ( 3 x + 13 − 2 y )
10. Which of the functions corresponds to the graph?
Fall, 2019, V1.24
9. ______
10. ______
A. f ( x ) = −e x + 2
B. f ( x ) = e− x + 2
C. f ( x ) = e x + 2
D. f ( x ) = e x + 1
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College Algebra MATH 107
Fall, 2019, V1.24
11. Suppose that for a function f , the equation f (x) = 0 has no real-number solution.
Which of the following statements MUST be true?
11. ______
A.
B.
C.
D.
f (0) does not exist.
f has no x-intercepts.
f has no y-intercepts.
The graph of f is a horizontal line.
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) – 2
g(x) = f (x + 1) – 1
g(x) = f (x + 2) + 2
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College Algebra MATH 107
Fall, 2019, V1.24
SHORT ANSWER:
13. Multiply and simplify: (8 − 5i)(6 + i).
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+7
0.
x −1
Answer: ________
Answer: ________
15. A can of soda at 83 F. is placed in a refrigerator that maintains a constant temperature of 37
F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by
T(t) = 37 + 46e – 0.058 t
Find the temperature of the soda 10 minutes after it is placed in the refrigerator. (Round to the
nearest degree.)
Answer: ________
1
16. Find the value of the logarithm: log3   .
9
17. Solve:
67 x−3 = 36 .
Answer: ________
Answer: ________
18. Suppose $8,500 is invested in an account at an annual interest rate of 2.3% compounded
continuously. How long (to the nearest tenth of a year) will it take the investment to double in
size?
Answer: ________
19. Let f (x) = x2 + 14x + 44.
(a) Find the vertex.
Answer: ________
(b) State the range of the function.
Answer: ________
(c) On what interval is the function increasing?
Answer: ________
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College Algebra MATH 107
Fall, 2019, V1.24
20. Consider the polynomial P(x), shown in both standard form and factored form.
(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, 2019, V1.24
3x 2 + 3
.
x2 − 4
(a) State the domain.
Answer: _________________
(b) State the vertical asymptote(s).
Answer: _________________
(c) State the horizontal asymptote.
Answer: _________________
3x 2 + 3
(d) Which of the following represents the graph of f ( x) = 2
?
x −4
GRAPH A.
GRAPH B.
GRAPH C.
GRAPH D.
Answer: ______________
Page 9 of 11
College Algebra MATH 107
Fall, 2019, V1.24
SHORT ANSWER, with work required to be shown, as indicated.
22. Let f (x) = x − 12 and g ( x) =
x −8 .
 f 
(a) Find  (9) . Show work.
g
(b) Find the domain of the quotient function
f
. Explain.
g
23. Points (–2, 3) and (6, –1) 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 (5, –6) and (1, 10). Write the
equation in slope-intercept form. Show work.
25. Lena, a resident of Metropolis, pays Metropolis an annual tax of $45 plus 1.8% of her annual
income. If Lena paid $1,548 in tax, what was Lena’s income? Show work.
26. Let f (x) = 2×2 + 9 and g(x) = x – 3.
(a) Find the composite function ( f  g )(x) and simplify. Show work.
(b) Find ( f o g ) (−2) . Show work.
27. Find the exact solutions and simplify as much as possible: 3×2 = 2 + 8x. Show work.
1
28. Given the function f ( x) = 3 + x , find a formula for the inverse function. Show work.
8
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College Algebra MATH 107
Fall, 2019, V1.24
29. The fuel efficiency F for a particular car is given by
F(x) = –0.02 x2 + 1.56 x + 5.8
where x is the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel
efficiency in miles per gallon (mpg).
(a) What is the fuel efficiency if the car’s speed is 20 mph?
(b) What speed will yield the maximum fuel efficiency? Show work.
30. Solve:
x + 13
84
+ 2
= 0 . Show work.
x + 6 x − 36
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