MATH 107 University of Maryland Global Campus College Algebra Final Exam

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Math 107 Final Exam Spring 2020
Professor: Dr. Kamal Hennayake
This is an open-book exam. You may only 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. (Work not required to be shown)
Problems $13 – 25 are Short Answer. (Work not required to be shown)
Problems #26 – 30 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1) Find the coordinates of the vertex of the graph of the function.
𝑓(π‘₯) = βˆ’2π‘₯ 2 βˆ’ 4π‘₯ + 8
A. (βˆ’1, 10)
B. (βˆ’1, 14)
C. (1, 2)
D. (10, βˆ’1)
E. (2, 1)
2) What is the end behavior of the graph?
A.
left -negative, right -positive
B.
left -positive, right –positive
C.
left -negative, right –negative
D.
left -positive, right -negative
3) Determine if the function is Odd, Even, or neither.
𝑓(π‘₯) = βˆ’
A. Odd
B. Even
2
+ 4π‘₯
3π‘₯
C. Neither
Math 107
Final Exam
Page 2
4) What is the least possible degree of the polynomial graphed below?
A.
2
B.
3
C.
4
D.
5
E.
6
4) Select the choice that is a graph of the function.
𝑓(π‘₯) = 6
π‘₯βˆ’1
(π‘₯ + 3)(π‘₯ βˆ’ 2)
(A)
(B)
(C)
(D)
6) Solve the equation.
3π‘₯ = 81
A. 2
B. 3
C. 4
D. 5
Math 107
Final Exam
Page 3
7) Starting with the graph of 𝑓(π‘₯) = 7π‘₯ , write the equation of the graph that results from shifting f(x) 8 units to
the left.
A. 𝑓(π‘₯) = 7π‘₯+8
B. 𝑓(π‘₯) = 7π‘₯βˆ’8
C. 𝑓(π‘₯) = 7π‘₯ + 8
D. 𝑓(π‘₯) = 7π‘₯ βˆ’ 8
E. 𝑓(π‘₯) = 8 βˆ™ 7π‘₯
8) What is the number of real zeros of the polynomial graphed below?
A. 3
B. 4
C. 5
D. 6
E. 7
9) Match the function with its graph. 𝑓(π‘₯) = βˆ’2(π‘₯ + 1)2 + 5
A.
C.
B.
D.
Math 107
Final Exam
Page 4
10) Which of the following criteria must be true about a function in order for that function to have an inverse?
1
𝑓 βˆ’1 (π‘₯) = 𝑓(π‘₯)
i.
ii.
iii.
iv.
𝑓(𝑓 βˆ’1 (π‘₯)) = π‘₯ and 𝑓 βˆ’1 (𝑓(π‘₯)) = π‘₯
The function passes the horizontal line test
The function is one-to-one
A. ii only
B. ii, iii, iv
C. ii, iii
D. i, ii, iii, and iv
11) Which of the following statements indicate when c is a zero of a polynomial function f(x)?
i)
ii)
iii)
iv)
c is the x-value of an x-intercept of 𝑓(π‘₯).
c is a solution to f(x) = 0; that is f(c) = 0.
c is the function value of f(0); that is, f(0) = c.
c produces a remainder of 0 when f(x) is divided by x – c; that if 𝑓(π‘₯) = (π‘₯ βˆ’ 𝑐)𝑄(π‘₯)
A. i, iii, iv
B. i, ii, iv
C. i, ii, iii, and iv
D. i, ii
12) Use the graph of the rational function to find the requested information.
As π‘₯ β†’ 3βˆ’ , 𝑓(π‘₯) β†’?
A.
∞
B.
βˆ’βˆž
C.
0
D.
3
E.
βˆ’3
SHORT ANSWER (Work not required to be shown)
13) Give the domain of 𝑓(π‘₯) = 3 + 7√14 βˆ’ 4π‘₯ in interval notation.
14) The point (βˆ’12, βˆ’18) is on the graph of 𝑦 = 𝑓(π‘₯)
1
a. A point on the graph of 𝑦 = 𝑔(π‘₯), where 𝑔(π‘₯) = 3 𝑓(π‘₯) + 15
b. A point on the graph of 𝑦 = 𝑔(π‘₯), where 𝑔(π‘₯) = 𝑓(12 βˆ’ π‘₯)
c. A point on the graph of 𝑦 = 𝑔(π‘₯), where 𝑔(π‘₯) = βˆ’2𝑓(βˆ’3π‘₯)
15) Tell whether the vertex is a maximum or a minimum. 𝑓(π‘₯) = βˆ’10π‘₯ 2 βˆ’ 81π‘₯ βˆ’ 811
Math 107
Final Exam
Page 5
16) Consider the function graphed below. Answer the followings. Join multiple intervals with a union if
needed. For example: the domain of the function is (βˆ’βˆž, ∞).
a. Give the interval(s) where the function is increasing.
b. Give the interval(s) where the function is decreasing.
c. Give the interval(s) where the function is constant.
d. Give the range of the function using interval notation.
17) Complete the description of the piecewise function graphed below.
𝑖𝑓
𝑓(π‘₯) =
𝑖𝑓
{
𝑖𝑓
18) Consider the function 𝑓(π‘₯) = 102|π‘₯ + 2| βˆ’ 20400 to find the intercepts.
a. Find the x-intercept(s) (if any as point(s)).
b. Find the y-intercept (if any as a point).
19) Determine an equation for the pictured graph. Write your answer in factored form. Do not expand the
equation.
20) Write an equation for a rational function with:
Vertical asymptotes at x = 6 and x = 5. The x intercepts at x = -5 and x = 3. Horizontal asymptote at y = 5
Math 107
Final Exam
Page 6
21) Solve the following quadratic inequality. βˆ’π‘₯ 2 + π‘₯ ≀ 132. Write your answer in interval notation.
1
22) Write log 𝑏 2 = βˆ’ 2 in exponential form.
23) Solve the equation log π‘Ž π‘Žβˆ’21 = π‘₯ for x.
24) The number of bacteria in a culture is given by the function 𝑁(𝑑) = 9050𝑒 0.45𝑑 . Where time is measured in
hours.
a. What is the relative rate of growth of this bacterium population?
b. What is the initial population of the culture?
c. How many bacteria will the culture contain in five days?
25) Given that 𝑓(π‘₯) = βˆ’π‘₯ 2 + 5π‘₯ and 𝑔(π‘₯) = π‘₯ βˆ’ 7 calculate the followings.
a. (𝑓 ∘ 𝑔)(βˆ’5)
b. (𝑔 ∘ 𝑓)(βˆ’5)
SHORT ANSWERS WITH WORK REQUERED TO BE SHOWN AS INDICATED.
26) Solve the equation for x? Show work clearly.
log 3 (π‘₯ + 3) = log 3 π‘₯ + log 3 3
27) The population of the world in 1987 was 5 billion and the relative growth rate was estimated at 2 percent
per year. Assuming that the world population follows an exponential growth model, find the projected world
population in 2025. Round your answer to 2 decimal places in billions. Show work clearly.
2
4
28) Let 𝑓(π‘₯) = π‘₯βˆ’3 and 𝑔(π‘₯) = π‘₯βˆ’5.
a. Find (𝑓 ∘ 𝑔)(π‘₯) Show work clearly.
b. Find and the domain of (𝑓 ∘ 𝑔)(π‘₯). Justify your answer.
29) Solve the rational inequality. Write your answer in interval notation. Show work clearly.
π‘₯βˆ’8
≀1
π‘₯+9
2π‘₯
30) Find the inverse function of 𝑓(π‘₯) = π‘₯+7. Show work clearly.
Math 107 Final Examination
Spring, 2020
1
Math 107 College Algebra
Name______________________________
Final Examination: Spring, 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 #1-12 are multiple choice. Record your choice for each problem.
Problems #13-25 are short answer. Record your answer for each problem.
Problems #26-30 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 plaintext 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___________________
Math 107 Final Examination
Spring, 2020
MULTIPLE CHOICE. Record your answer choices.
1.
7.
2.
8.
3.
9.
4.
10.
5.
11.
6.
12.
SHORT ANSWER. Record your answers below.
13.
14.
(a)
(b)
(c)
15.
16.
(a)
(b)
(c)
(d)
17.
(a)
(b)
(c)
(d)
(e)
(f)
18.
(a)
(b)
2
Math 107 Final Examination
19.
20.
21.
22.
23.
24.
(a)
(b)
(c)
25.
(a)
(b)
Spring, 2020
3
Math 107 Final Examination
Spring, 2020
SHORT ANSWER with Work Shown. Record your answers and work.
Problem
Number
Solution
Answer:
Work:
26
Answer:
Work:
27
4
Math 107 Final Examination
Answers:
(a)
(b)
Work for part (a):
28
Justification for part (b):
Answer:
Work:
29
Answer:
Work:
30
Spring, 2020
5
Math 107 Final Examination
Spring, 2020
1
Math 107 College Algebra
Name______________________________
Final Examination: Spring, 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 #1-12 are multiple choice. Record your choice for each problem.
Problems #13-25 are short answer. Record your answer for each problem.
Problems #26-30 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 plaintext 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___________________
Math 107 Final Examination
Spring, 2020
MULTIPLE CHOICE. Record your answer choices.
1.
7.
2.
8.
3.
9.
4.
10.
5.
11.
6.
12.
SHORT ANSWER. Record your answers below.
13.
14.
(a)
(b)
(c)
15.
16.
(a)
(b)
(c)
(d)
17.
(a)
(b)
(c)
(d)
(e)
(f)
18.
(a)
(b)
2
Math 107 Final Examination
19.
20.
21.
22.
23.
24.
(a)
(b)
(c)
25.
(a)
(b)
Spring, 2020
3
Math 107 Final Examination
Spring, 2020
SHORT ANSWER with Work Shown. Record your answers and work.
Problem
Number
Solution
Answer:
Work:
26
Answer:
Work:
27
4
Math 107 Final Examination
Answers:
(a)
(b)
Work for part (a):
28
Justification for part (b):
Answer:
Work:
29
Answer:
Work:
30
Spring, 2020
5

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