Quiz08
Please show your work. There should be only one document. The answer sheet is provided and you write answers there. You may attach an extra sheet if need be but is not necessary. . You may take as much or as little time as you need, within the three-day period
You may type your answers and work, or handwrite and scan it.
Math 107 Final Examination
Fall 2020 1
Math 107 College Algebra
Name______________________________
Final Examination: Fall 2020 Instructor __________________________
Answer Sheet
Instructions:
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.
Record your answers and work in this document.
There are 30 problems.
Problems #1-11 are multiple choice. Record your choice for each problem.
Problems #12-21 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 plain-text 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.
You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Your exam will receive a zero grade unless you complete the following honor statement.
Please sign (or type) your name below the following honor statement:
I have completed this final examination myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this final examination.
Name _____________________ Date___________________
MULTIPLE CHOICE. Record your answer choices.
1. 7.
2. 8.
3. 9.
4. 10.
5. 11.
6.
SHORT ANSWER. Record your answers below.
12.
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
22
Answers:
(a)
(b)
Work/for part (a) and explanation for part (b):
23
Answers:
(a)
(b)
(c)
Work for part (a):
24
Answer:
Work:
25
Answer:
Work:
26
Answers:
(a)
(b)
Work for part (a) and for part (b):
27
Answer:
Work:
28
Answer:
Work:
29
Answers:
(a)
(b)
Work for (b):
30
Answer:
Work:
CollegeAlgebra MATH 107 Fall 2020
Page 1 of 11
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. The exam starts at 12:01 on
Sunday 10/11/2020 and must finish by 10/13/2020 11:59 P.M. Please use the answer sheet.
Show your work, plot the graph using DESMOS or TI-calculator. Please do not submit any
extra Excel or file or file file.
Thank you. Sincerely, Dr. K.S. Altmayer
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #1–11 are Multiple Choice.
Problems #12–21 are Short Answer. (Show some)
Problems #22–30 are Short Answer with work required to be shown.
1. Determine the domain and range of the piecewise function. 1.
A. Domain [–1, 3]; Range [–3, 1]
B. Domain [–1, 1]; Range [–1, 1]
C. Domain [–3, 1]; Range [–1, 3]
D. Domain [1/2, 3/2]; Range [0, 1]
2. Solve: = − x
2.
A. –8
B. –8, 3
C. 1/6
D. No solution
4
2
-4
-2 2 4
-2
-4
College Algebra MATH 107 Fall 2020
Page 2 of 11
3. Determine the interval(s) on which the function is decreasing. Show work. 3.
A. (–∞, – 4) and (1, ∞)
B. (– 4, –1.2)
C. (–∞, –2)
D. (– 5.5, –2)
4. Determine whether the graph of
the x-axis, or the y-axis.
y = x − 4 is symmetric with respect to the origin,
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: | 5 – 6x | ≤ 13. Show work. 5.
A. (–∞, −4/3] ∪ [3, ∞)
B. [3, ∞)
C. [–3, 4/3]
D. [–4/3, 3]
College Algebra MATH 107 Fall 2020
Page 3 of 11
6. Which of the following represents the graph of 4x − 9y = 36 ? Show work. 6.
A. B.
C. D.
College Algebra MATH 107 Fall 2020
Page 4 of 11
7. Write a slope-intercept equation for a line parallel to the line x – 4y = 6 which passes through
the point (12, –3). Show work. 7.
A. y = − 4x + 45
B. y = 1 x − 3
4
C. y = 1 x − 6
4
D. y = − 1 x −1
4
E. None
8. Does the graph below represent a function and is it one-to-one? Show work. 8.
A. It is a function and it is one-to-one.
B. It is not a function, but it is one-to-one.
C. It is a function but not one-to-one.
D. It is not a function and it is not one-to-one.
College Algebra MATH 107 Fall 2020
Page 5 of 11
9. Solve the equation for x using the One-to-One Property.
a. –11
b. 0
c. The equation has no solution.
d. –9
e. 11
10. Which of the functions corresponds to the graph? Show work, attach screenshot
10.
a. f (x) = −ex + 2
b. f (x) = e−x + 2
c. f (x) = ex + 2
d. f (x) = e−x +1
College Algebra MATH 107 Fall 2020
Page 6 of 11
11. 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)? show work.
12.
y = f (x) y = g(x)
A. g(x) = f (x + 1) – 1
B. g(x) = f (x + 1) + 1
C. g(x) = f (x – 1) – 1
D. g(x) = f (x – 1) + 1
4
2
-4 -2 2 4
-2
-4
-4 -2 2 4
-2
-4
4
2
College Algebra MATH 107 Fall 2020
Page 7 of 11
12. Multiply and simplify: (9 + i)2.
Write the answer in the form a + bi, where a and b are real numbers.
Answer:
13. Solve, and write the answer in interval notation:
x + 7
≥ 0 .
Answer:
x −1
14. A bowl of soup at 170° F. is placed in a room of constant temperature of 60° F. The
temperature T of the soup t minutes after it is placed in the room is given by
Find the temperature of the soup 16 minutes after it is placed in the room. (Round to the nearest
degree.)
Answer:
15. Solve: 44x− 9 =16. Answer:
16. Suppose $6,500 is invested in an account at an annual interest rate of 3.7% compounded
continuously. How long (to the nearest tenth of a year) will it take the investment to double in
size? Answer:
17. Determine the zeros (if any) of the rational function
.
a.
b. no zeros
c.
d.
e.
Answer:
College Algebra MATH 107 Fall 2020
Page 8 of 11
18. Use the position equation to write a
function that represents the situation and give the average
velocity of the object from time t1 to time t2.
An object is thrown upward from a height of 174 feet at a
velocity of 1 feet per second.
t1 = 1, t2 = 5
a.
b.
c.
d.
e.
19. Let f (x) = x2 − 12x + 28.
(a) Find the vertex.
(b) State the range of the function. Answer:
(c) On what interval is the function increasing? Answer:
College Algebra MATH 107 Fall 2020
Page 9 of 11
20. Consider the polynomial P(x), shown in both standard form and factored form.
P(x)= 1
10
𝑥𝑥4 − 1
2
𝑥𝑥3 − 7
10
𝑥𝑥2 + 41
10
𝑥𝑥 − 3 = 1
10
(𝑥𝑥 + 3)(𝑥𝑥 − 1)(𝑥𝑥 − 2)(𝑥𝑥 − 5)
(a) Which sketch illustrates the end behavior of the polynomial function?
Answer:
(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
A.
vvvv
B.
vvvv
C.
vvvv
D.
vvvv
College Algebra MATH 107 Fall 2020
Page 10 of 11
GRAPH C GRAPH D
College Algebra MATH 107 Fall 2020
Page 11 of 11
21. Let
f (x) =
3×2 − 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
the function f(x)=3𝑥𝑥
2−3
𝑥𝑥2−4
? Answer__________
Ans
wer:
GRAPH A. GRAPH B.
College Algebra MATH 107 Fall 2020
Page 12 of 11
GRAPH C. GRAPH D.
College Algebra MATH 107 Fall 2020
Page 13 of 11
SHORT ANSWER, with work required to be shown, as indicated.
22. Use a graphing utility to graph the parabola. Plot the graph with all the axes and intersection
points if any. Create a table for the values of x and y.
23. Points (–5, 2) and (–1, 8) 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 (4, –3) and (6, –7). Write the
equation in slope-intercept form. Show work and plot the graph.
25. A salesperson earns a base salary of $1,260 per month and a commission of 5.6% on the
amount of sales made. If the salesperson has a paycheck of $3,959.20 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 + 3.
(a) Find the composite function ( f οg)(x) and simplify. Show work.
(b) Find ( f o g )(−5) . Show work.
27. Find the exact solutions and simplify as much as possible: 8×2 + 11 = 20x. Show work.
28. Given the function f (x) = 7 +
1 x , find a formula for the inverse function. Show work.
2
College Algebra MATH 107 Fall 2020
Page 14 of 11
29. Donut Delights, Inc. has determined that when x donuts are made daily, the
profit P (in dollars) is given by
(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. Find a polynomial with real coefficients that has zeros –10, 2i, and –2i.
a.
b.
c.
d.
e.
- MATH 107 FINAL EXAMINATION
- Neither collaboration nor consultation with others is allowed. The exam starts at 12:01 on Sunday 10/11/2020 and must finish by 10/13/2020 11:59 P.M. Please use the answer sheet. Show your work, plot the graph using DESMOS or TI-calculator. Please do …
MULTIPLE CHOICE
SHORT ANSWER: Show some work and/or attach screenshot.
T(t) = 60 + 110 e – 0.075 t
SHORT ANSWER, with work required to be shown, as indicated.
Show work.
P(x) = –0.002 x2 + 4.5x – 1700