 # MATH 107 UMUC Final Examination

College Algebra MATH 107 Fall, 2014, V1.3
Page 1 of 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.
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. ______
A. Domain [–1, 1]; Range [1, 3]
B. Domain [–1, 3]; Range [–2, 2]
C. Domain [–2, 2]; Range [–1, 3]
D. Domain [–3/2, –1/2]; Range [–1, 0]

2. Solve: 15 - 2x = 6 - x
A. 9
B. 3
C. 3, 7
D. No solution

3. Determine the interval(s) on which the function is increasing. 3. ______
A. (-1.3, 1.3)
B. (1, 3)
C. (-2.5, 1) and (4.5,¥)
D. (-¥,-1) and (3,¥)

4. Determine whether the graph of y = |x -7| is symmetric with respect to the origin,
the x-axis, or the y-axis. 4. ______
A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and
not symmetric with respect to the origin
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. symmetric with respect to the origin only

5. Solve, and express the answer in interval notation: | 8 – 5x | £ 12. 5. ______
A. [– 4, 4/5]
B. (–¥, – 4/5] È [4, ¥)
C. [– 4/5, 4]
D. [– 4/5, ¥)

6. Which of the following represents the graph of 3x + 7y = 21 ? 6. ______
A.
B.
C.
D.

7. Write a slope-intercept equation for a line parallel to the line x + 8y = 6 which passes through
the point (24, –5). 7. ______
A. y = -8x -197
B.
C.
D.

8. Does the graph below represent a function and is it one-to-one? 8. ______
A. It is a function but not one-to-one.
B. It is a function and it is one-to-one.
C. It is not a function and it is not one-to-one.
D. It is not a function but it is one-to-one.

9. Express as a single logarithm: log (x + 2) + log 1 – 3 log y 9. ______
A.
B.
C.
D. log ( x + 3- 3y)

10. Which of the functions corresponds to the graph? 10. ______
A. ( ) 1 x f x = -e -
B. ( ) 1 x f x e- = -
C. ( ) 1 x f x = e -
D. ( ) 2 x f x e- = -

11. The percentage score on a test varies directly as the number of correct responses. Julie
answered 21 questions correctly and earned a score of 70%. What would Julie’s percentage score
A. 73%
B. 77%
C. 80%
D. 96%

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. ______
y = f (x) y = g(x)
A. g(x) = f (x + 2) + 2
B. g(x) = f (x + 1) – 2
C. g(x) = f (x + 1) – 1
D. g(x) = f (x – 1) – 2

13. Multiply and simplify: (7 – 3i)(5 + i).
Write the answer in the form a + bi, where a and b are real numbers. Answer: ________

14. Solve, and write the answer in interval notation: . Answer: ________

15. A bowl of soup at 195° F. is placed in a room of constant temperature of 65° F. The
temperature T of the soup t minutes after it is placed in the room is given by
T(t) = 65 + 130 e^(–0.075 t)
Find the temperature of the soup 6 minutes after it is placed in the room. (Round to the nearest
degree.)

16. Find the value of the logarithm: . Answer: ________

17. Solve: 8^(7x-1) = 64 . Answer: ________

18. Suppose \$2,500 is invested in an account at an annual interest rate of 5.3% compounded
continuously. How long (to the nearest tenth of a year) will it take the investment to double in

19. Let f (x) = x^2 - 10x + 28.
(a) Find the vertex. Answer: ________
(b) State the range of the function. Answer: ________
(c) On what interval is the function decreasing? Answer: ________

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?
(b) State the zeros of the function. Answer: ________________
(c) State the y-intercept. Answer: ________________
(d) State which graph below is the graph of P(x). Answer: ________
GRAPH A GRAPH B
GRAPH C GRAPH D

21. Let f(x)=.
(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 . Answer: ______________
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.

SHORT ANSWER, with work required to be shown, as indicated.
22. Simplify: . Show work.

23. Points (5, –1) and (9, 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 of the circle?
(c) What is the equation of the circle?

24. Find the equation for a line which passes through the points (3, 4) and (1, 8). Write the
equation in slope-intercept form. Show work.

25. Carl, a resident of Metropolis, pays Metropolis an annual tax of \$90 plus 1.3% of his annual
income. If Carl paid \$909 in tax, what was Carl’s income? Show work.

26. Let f (x) = 2x^2 – 8 and g(x) = x – 3.
(a) Find the composite function ( f  g)(x) and simplify. Show work.
(b) Find ( f  g ) (-1) . Show work.

27. Find the exact solutions and simplify as much as possible: 8x^2 + 13 = 20x. Show work.

28. Given the function, find a formula for the inverse function. Show work.

29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P is given by
P(x) = –0.002 x^2 + 4.5x – 170
(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: . Show work.

Step-by-step solutions to thirty questions leading to the final answers. All equations are written in Microsoft Office 2013 Equation Editor.

Subjects: Mathematics -> Algebra
Topic: College Algebra MATH 107 UMUC Final Exam
Level: College
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### Math107, MATH 107, final, exam, UMUC, College, Algebra

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## Math107, MATH 107, final, exam, UMUC, College, Algebra

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