3D Represent.docx

3D Representation
Read chapter 10 in Computer Science: note especially section
10.2. Create a 2-page document which will summarize the three
steps involved in producing an image using 3D graphics. After
you describe each step, give a good example of each. The
examples should be different from the one given in the text.

Find a recent news article (not a tutorial or description) that
relates to 3D graphics. Explain how any aspect of the news
article relates to one of the steps you summarized above.
The document should be clear and concise, free from syntax and
semantic errors.
Please submit the document on time please.
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 #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 [– 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
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]

of 11
6. Which of the following represents the graph of 7x + 4y = 28
? 6. ______
A. B.
C. D.
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.
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= +
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
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:
________
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
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.

Page 10 of 11
SHORT ANSWER, with work required to be shown, as
indicated.
22. Let f (x) = x – 7 and 3)( −= xxg .
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 Dave’s 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.
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 company’s profit if 1,000 donuts are made
daily?
(b) How many donuts should be made daily in order to
maximize the company’s profit? Show
work.
30. Solve:
2
7 24
0
3 9
x
x x
+
+ =
+ −
. Show work.

Math 107 Final Examination Spring, 2017 1
Math 107 College Algebra
Name______________________________
Final Examination: Spring, 2017 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 #13-21 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. 12.
SHORT ANSWER. Record your answers below.
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):

(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:

29
Answers:
(a)
(b)
Work for (b):

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