Math Algebra 107
College Algebra MATH 107 Spring, 2017, V.1.3
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. Record your answers and work on the separate answer sheet provided.
There are 30 problems. Problems #112 are Multiple Choice. Problems #1321 are Short Answer. (Work not required to be shown) Problems #2230 are Short Answer with work required to be shown. MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function. 1. ______
A. Domain [ 3, 3]; Range [ 1, 3] B. Domain [ 3, 1]; Range [ 3, 3] C. Domain [ 1, 0.5]; Range [1, 0]
D. Domain (?, 3]; Range [1, ?)
2. Solve: 10 3x x? = ? 2. ______
A. 5, 2 B. 5/2 C. 5 D. No solution
2 4 -4
-2
-4
2
4
-2
College Algebra MATH 107 Spring, 2017, V.1.3
Page 2 of 11
3. Determine the interval(s) on which the function is increasing. 3. ______
A. (?, 1) B. ( 2, 2)
C. (?, 3) and (1, ?)
D. ( 4.5, 1) and (2.5, ?)
4. Determine whether the graph of ( ) 2
4xy ?= 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: | 6 5x | ? 14. 5. ______
A. (?, ?8/5] ? [4, ?)
B. (?, 8/5]
C. [4, ?) D. [8/5, 4]
College Algebra MATH 107 Spring, 2017, V.1.3
Page 3 of 11
6. Which of the following represents the graph of 7x + 4y = 28 ? 6. ______ A. B.
C. D.
College Algebra MATH 107 Spring, 2017, V.1.3
Page 4 of 11
7. Write a slope-intercept equation for a line parallel to the line x 3y = 5 which passes through the point (6, 8). 7. ______
A. 1
8 3
y x= ?
B. 1
10 3
y x= ?
C. 1
6 3
y x= ? ?
D. 3 10y x= ? +
8. Which of the following best describes the graph? 8. ______
A. It is a function and it is one-to-one. B. It is a function but not one-to-one. C. It is not a function but it is one-to-one. D. It is not a function and it is not one-to-one.
College Algebra MATH 107 Spring, 2017, V.1.3
Page 5 of 11
9. Write as an equivalent expression: log (x 1) 3 log y + log 1 9. ______
A. log 3
x
y
? ? ? ? ? ?
B. log( 1)
log(3 )
x
y
?
C. 3
1 log
x
y
? ?? ? ? ? ?
D. ( )log 3x y?
10. Which of the functions corresponds to the graph? 10. ______
A. ( ) 2xf x e= ? +
B. ( ) 2xf x e?= +
C. ( ) 1xf x e?= +
D. ( ) 2xf x e= +
College Algebra MATH 107 Spring, 2017, V.1.3
Page 6 of 11
11. Suppose that a function f has exactly two x-intercepts. Which of the following statements MUST be true? 11. ______ A. f is a linear function. B. f is a quadratic function. C. f is an invertible function. D. 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. ______
y = f (x) y = g(x) A. g(x) = f (x + 1) 2 B. g(x) = f (x 2) + 1 C. g(x) = f (x 1) + 2 D. g(x) = f (x + 2) + 1
2 4 -2 -4
-2
-4
2
4
2 4 -2 -4
-2
-4
2
4
College Algebra MATH 107 Spring, 2017, V.1.3
Page 7 of 11
SHORT ANSWER:
13. Multiply and simplify: (5 ? i)(8 + 3i). 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: 2
0 9
x
x
+ ?
? . Answer: ________
15. A bowl of soup at 175° F. is placed in a room of constant temperature of 70° F. The temperature T of the soup t minutes after it is placed in the room is given by
T(t) = 70 + 105 e 0.075 t
Find the temperature of the soup 18 minutes after it is placed in the room. (Round to the nearest degree.) Answer: ________
16. Find the value of the logarithm: 7 1
log 49
? ? ? ? ? ?
. Answer: ________
17. Solve: 3 72 4x+ = . Answer: ________
18. Suppose $4,600 is invested in an account at an annual interest rate of 3.5% 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) = x 2 + 10x + 27.
(a) Find the vertex. Answer: ________ (b) State the range of the function. Answer: ________ (c) On what interval is the function decreasing? Answer: ________
College Algebra MATH 107 Spring, 2017, V.1.3
Page 8 of 11
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?
Answer: ________
(b) State the y-intercept. Answer: ________________
(c) State the zeros of the function. Answer: ________________
(d) State which graph below is the graph of P(x). Answer: ________
GRAPH A
GRAPH B
GRAPH C
GRAPH D
A.
B. C. D.
vvvv
vvvv vvvv vvvv
College Algebra MATH 107 Spring, 2017, V.1.3
Page 9 of 11
21. Let 2 4
( ) 3
x f x
x
? =
? .
(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 2 4
( ) 3
x f x
x
? =
? ? Answer: ______________
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
College Algebra MATH 107 Spring, 2017, V.1.3
Page 10 of 11
SHORT ANSWER, with work required to be shown, as indicated.
22. Let f (x) = x 7 and 3)( ?= xxg .
(a) Find )12(?? ?
? ?? ?
?
g
f . Show work.
(b) Find the domain of the quotient function g
f . Explain.
23. Points (7, 9) and (3, 5) 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, 7) and (2, 1). Write the equation in slope-intercept form. Show work.
25. Dave, a resident of Metropolis, pays Metropolis an annual tax of $58 plus 1.9% of his annual income. If Dave paid $1,255 in tax, what was Daves income? Show work.
26. Let f (x) = 2x 2 8 and g(x) = x 4.
(a) Find the composite function ))(( xgf o and simplify. Show work.
(b) Find ( ) (1)f go . Show work.
27. Find the exact solutions and simplify as much as possible: 6x 2 + 5 = 12x. Show work.
28. Given the function 1
( ) 5 7
f x x= + , find a formula for the inverse function. Show work.
College Algebra MATH 107 Spring, 2017, V.1.3
Page 11 of 11
29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P, in dollars, is given by
P(x) = 0.001 x 2 + 3.2x 1450
(a) What is the companys profit if 1,000 donuts are made daily? (b) How many donuts should be made daily in order to maximize the companys profit? Show work.
30. Solve: 2
7 24 0
3 9
x
x x
+ + =
+ ? . Show work.
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math107_final_exam_spring2017harley.pdf
Home>Mathematics homework help>Math Algebra 107
College Algebra MATH 107 Spring, 2017, V.1.3
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. Record your answers and work on the separate answer sheet provided.
There are 30 problems. Problems #112 are Multiple Choice. Problems #1321 are Short Answer. (Work not required to be shown) Problems #2230 are Short Answer with work required to be shown. MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function. 1. ______
A. Domain [ 3, 3]; Range [ 1, 3] B. Domain [ 3, 1]; Range [ 3, 3] C. Domain [ 1, 0.5]; Range [1, 0]
D. Domain (?, 3]; Range [1, ?)
2. Solve: 10 3x x? = ? 2. ______
A. 5, 2 B. 5/2 C. 5 D. No solution
2 4 -4
-2
-4
2
4
-2
College Algebra MATH 107 Spring, 2017, V.1.3
Page 2 of 11
3. Determine the interval(s) on which the function is increasing. 3. ______
A. (?, 1) B. ( 2, 2)
C. (?, 3) and (1, ?)
D. ( 4.5, 1) and (2.5, ?)
4. Determine whether the graph of ( ) 2
4xy ?= 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: | 6 5x | ? 14. 5. ______
A. (?, ?8/5] ? [4, ?)
B. (?, 8/5]
C. [4, ?) D. [8/5, 4]
College Algebra MATH 107 Spring, 2017, V.1.3
Page 3 of 11
6. Which of the following represents the graph of 7x + 4y = 28 ? 6. ______ A. B.
C. D.
College Algebra MATH 107 Spring, 2017, V.1.3
Page 4 of 11
7. Write a slope-intercept equation for a line parallel to the line x 3y = 5 which passes through the point (6, 8). 7. ______
A. 1
8 3
y x= ?
B. 1
10 3
y x= ?
C. 1
6 3
y x= ? ?
D. 3 10y x= ? +
8. Which of the following best describes the graph? 8. ______
A. It is a function and it is one-to-one. B. It is a function but not one-to-one. C. It is not a function but it is one-to-one. D. It is not a function and it is not one-to-one.
College Algebra MATH 107 Spring, 2017, V.1.3
Page 5 of 11
9. Write as an equivalent expression: log (x 1) 3 log y + log 1 9. ______
A. log 3
x
y
? ? ? ? ? ?
B. log( 1)
log(3 )
x
y
?
C. 3
1 log
x
y
? ?? ? ? ? ?
D. ( )log 3x y?
10. Which of the functions corresponds to the graph? 10. ______
A. ( ) 2xf x e= ? +
B. ( ) 2xf x e?= +
C. ( ) 1xf x e?= +
D. ( ) 2xf x e= +
College Algebra MATH 107 Spring, 2017, V.1.3
Page 6 of 11
11. Suppose that a function f has exactly two x-intercepts. Which of the following statements MUST be true? 11. ______ A. f is a linear function. B. f is a quadratic function. C. f is an invertible function. D. 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. ______
y = f (x) y = g(x) A. g(x) = f (x + 1) 2 B. g(x) = f (x 2) + 1 C. g(x) = f (x 1) + 2 D. g(x) = f (x + 2) + 1
2 4 -2 -4
-2
-4
2
4
2 4 -2 -4
-2
-4
2
4
College Algebra MATH 107 Spring, 2017, V.1.3
Page 7 of 11
SHORT ANSWER:
13. Multiply and simplify: (5 ? i)(8 + 3i). 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: 2
0 9
x
x
+ ?
? . Answer: ________
15. A bowl of soup at 175° F. is placed in a room of constant temperature of 70° F. The temperature T of the soup t minutes after it is placed in the room is given by
T(t) = 70 + 105 e 0.075 t
Find the temperature of the soup 18 minutes after it is placed in the room. (Round to the nearest degree.) Answer: ________
16. Find the value of the logarithm: 7 1
log 49
? ? ? ? ? ?
. Answer: ________
17. Solve: 3 72 4x+ = . Answer: ________
18. Suppose $4,600 is invested in an account at an annual interest rate of 3.5% 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) = x 2 + 10x + 27.
(a) Find the vertex. Answer: ________ (b) State the range of the function. Answer: ________ (c) On what interval is the function decreasing? Answer: ________
College Algebra MATH 107 Spring, 2017, V.1.3
Page 8 of 11
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?
Answer: ________
(b) State the y-intercept. Answer: ________________
(c) State the zeros of the function. Answer: ________________
(d) State which graph below is the graph of P(x). Answer: ________
GRAPH A
GRAPH B
GRAPH C
GRAPH D
A.
B. C. D.
vvvv
vvvv vvvv vvvv
College Algebra MATH 107 Spring, 2017, V.1.3
Page 9 of 11
21. Let 2 4
( ) 3
x f x
x
? =
? .
(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 2 4
( ) 3
x f x
x
? =
? ? Answer: ______________
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
College Algebra MATH 107 Spring, 2017, V.1.3
Page 10 of 11
SHORT ANSWER, with work required to be shown, as indicated.
22. Let f (x) = x 7 and 3)( ?= xxg .
(a) Find )12(?? ?
? ?? ?
?
g
f . Show work.
(b) Find the domain of the quotient function g
f . Explain.
23. Points (7, 9) and (3, 5) 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, 7) and (2, 1). Write the equation in slope-intercept form. Show work.
25. Dave, a resident of Metropolis, pays Metropolis an annual tax of $58 plus 1.9% of his annual income. If Dave paid $1,255 in tax, what was Daves income? Show work.
26. Let f (x) = 2x 2 8 and g(x) = x 4.
(a) Find the composite function ))(( xgf o and simplify. Show work.
(b) Find ( ) (1)f go . Show work.
27. Find the exact solutions and simplify as much as possible: 6x 2 + 5 = 12x. Show work.
28. Given the function 1
( ) 5 7
f x x= + , find a formula for the inverse function. Show work.
College Algebra MATH 107 Spring, 2017, V.1.3
Page 11 of 11
29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P, in dollars, is given by
P(x) = 0.001 x 2 + 3.2x 1450
(a) What is the companys profit if 1,000 donuts are made daily? (b) How many donuts should be made daily in order to maximize the companys profit? Show work.
30. Solve: 2
7 24 0
3 9
x
x x
+ + =
+ ? . Show work.
Applied Sciences
Architecture and Design
Biology
Business & Finance
Chemistry
Computer Science
Geography
Geology
Education
Engineering
English
Environmental science
Spanish
Government
History
Human Resource Management
Information Systems
Law
Literature
Mathematics
Nursing
Physics
Political Science
Psychology
Reading
Science
Social Science
Home
Homework Answers
Blog
Archive
Tags
Reviews
Contact
twitterfacebook
Copyright © 2022 SweetStudy.com
