Quiz 3 SU20 Math 107
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University of Maryland Global Campus (UMGC) *
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Course
107
Subject
Mathematics
Date
Apr 3, 2024
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docx
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________________________________ I have completed this assignment myself, working independently and not consulting anyone except the instructor. MATH 107 QUIZ 3 INSTRUCTIONS Summer 2020 Instructor: D. Zulli ●
The quiz is worth 100 points. There are 9 problems. This quiz is open book
and open notes . This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission.) You may take as much time as you wish, provided you turn in your quiz no later than Wednesday, July 14 at 11:59 p.m. ●
Show work/explanation where indicated. Answers without any work m ay earn little, if any, credit.
You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work. ●
General quiz tips and instructions for submitting work are posted in the Quizzes module. ●
If you have any questions, please contact me by e-mail. 1.
(6 points) For
each graph, is the graph symmetric with respect to the x-axis? y-axis? O rigin? ( No explanation required. Just circle Yes or No to each question. ) Symmetric with respect to the: x-axis? Yes or No y-axis? Yes or No Origin? Yes or No Symmetric with respect to the: x-axis? Yes or No y-axis? Yes or No Origin? Yes or No 2.
(6 points)
Let
f(x)
= |3x| - 9. a.
State the zero(s) of the function. b.
Which of the following is true? Circle the true statement.
i.
f
is an even function ii.
f is an odd function /
iii.
f is both even and odd iv.
f is neither even
nor odd 3.
(6 points)
Which
of the following equations does the graph represent? Show work or explanation. A.
y = 3
2
x
+ 3 B.
y = - 2
3
x
+ 3 C.
y =- 3
2
x
+ 3 D.
y = 2
3
x
+ 3 4.
(12 points)
Consider
the points (0, -1) and (3, 1 a.
Find the slope-intercept equation of the line passing through the two given points. Show work . b.
Graph the line you found in (a), either drawing it on the grid in the previous problem #3, or generating the graph electronically and attaching it. c.
Compare your line for this problem, #4b, with the line given in the previous problem #3. Are the two lines parallel, perpendicular, or neither parallel nor perpendicular? (The terms parallel and perpendicular are discussed on pages 166 and 167.) No
explanation required - just state the answer. 5.
(20 points)
James
wants to purchase jersey’s for his little league team. Company A charges $ 95 plus $16 per shirt. Company B charges $185 plus $13 per shirt. a.
State a linear function f(x)
that represents Company A’s total charge for an order of
x
shirts. /
b.
State a linear function g(x)
that represents Company B’s total charge for an order of
x
shirts. c.
James needs to purchase 32 shirts, as cheaply as possible. With which company should he place his order? Show
work and explanation. d.
For what number of shirts is the total charge exactly the same for both companies? Show algebraic work. e.
Fill in the blanks. Company A is the cheaper option if ______ ( choose less or more)
than ______ (
enter
number ) shirts are ordered. 6.
(8 points)
The
value of Jennifer’s stock portfolio is given by the function f(t)
= 51 + 72t − 3t 2 , where f(t)
is the value of the portfolio in hundreds of dollars
and t is the time in years. Find and interpret the average rate of change of f
over the interval {t| 5 ≤ t ≤ 11 } = [5, 11] .
Show work . 7.
(8 points)
A
graph of y = f(x) follows. No formula for f is given. Which graph (A, B, C, or D) represents the graph of y =
f (x+5) + 3? Explain
your choice. (Work not required.) y = f(x) /
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A. B. C. D. 8.
(20 points)
Consider
the graph of the piecewise defined function y = f(x)
pictured below. No explanation required.
a.
State the value of
f (1) b.
State the x-intercept(s), if any c.
State the y-intercept(s), if any d.
State the domain of the piecewise function. e.
State the range of the piecewise function. f.
State the interval(s) on which the function is increasing.
That is, for what x-values is the function increasing? /
g.
State the interval(s) on which the function is decreasing.
That is, for what x-values is the function decreasing? 9.
(14 points) Ice
cream sales at a local ice cream shop on a particular day are linearly related to the temperature as depicted in the following chart. The regression line is
y = 4.193x - 163.41 , where x is the
day’s (average) temperature and y is the total sales for the day. The value of r 2 is 0.7 . Ice Cream Sales with respect to Temperature Daily Sales Temperature in degrees a.
Use the regression line to estimate the daily sales when the temperature is 80 degrees. b.
Use the regression line to predict the daily sales when the temperature is 95 degrees. c.
What is the slope of the regression line and what are the units of measurement? In a sentence, interpret what the s lope is telling us, in the context of this real-world application. d.
What is the value of the correlation coefficient, r? Also, interpret its value: looking at the graph and size of r: Is the linear relationship positive
or negative
and do you judge the strength
of the linear relationship to be very strong, moderately strong, somewhat weak, or very weak? /