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| August 30, 2017

Question
MATH 107

Quiz 3

Section 1.6, 1.7, 2.1, 2.2, 2.5

November 7 Instructor: J. Uccellini

Instructions:

The quiz is worth 85 points. There are 9 problems. Your score on the quiz will be
converted to a percentage and posted in your Portfolio with comments.
This quiz is open book and open notes, and you may take as long as you like on it
provided that you submit the quiz no later than the due date posted in our course schedule
of the syllabus. You may refer to your textbook, notes, and online classroom materials,
but you may not consult anyone or any online resource.
You must show all of your work to receive full credit. If you do not show work, you
may earn only partial or no credit.
Please type your work in your copy of the quiz, or if you prefer, create a document
containing your work. Scanned work is also acceptable. Be sure to include your name in
the document. Review instructions for submitting your quiz in the Quizzes and Exams
Conference.
If you have any questions, please contact me by e-mail
(john.uccellini@faculty.umuc.edu).

At the end of your quiz you must sign the following dated statement with your name typed in lieu
of a signature. Without this signed statement you will receive a zero.
I have completed this exam myself, working independently and not consulting anyone except the
instructor. I have neither given nor received help on this exam.
Name:

Date:

Please remember to show ALL of your work on every problem. If there is no
work to show, then include a sentence or two explaining your answer.
NAME: _______________________________
¿
for−10 ≤ x ≤−2 −2< x ≤ 0
4−2 x
¿
1. (5 pts each) Consider the piecewise function
5 x +1
f ( x )= { ¿ for 0<x ≤ 10¿
a. Find

f (2)

b. Find

f (0)

2. (5 pts) 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 – 1) – 1 ?
EXPLAIN YOUR CHOICE.

(Grid supplied for scratch work; You are NOT required to submit your own graph)

Answer:______________ Explain why you chose your answer.

y = f (x)
4
2
– 4 2 2
4

4
2

2 4

GRAPH A (below)

4
2
– 4 2 2
4

GRAPH B (below)

4
2
2 4

4
2
GRAPH C (below)
– 4 2 2
4

– – 24
4 22
4

2 4

– – 24
4 22
4

4
2
GRAPH D (below)
– – 24
4 22
4

3. Let

a.

f ( x) x 3 2
Evaluate

b. Evaluate

c. Evaluate

(5 pts each)

f ( x)

f ( x)

. How does the graph of

. How does the graph of

f ( x)

. How does the graph of

f ( x)

f ( x)

compare to the graph of

compare to the graph of

f ( x)

compare to the graph of

f ( x )

f ( x)

?

?

f ( x )

?

3

4. (5 pts) Let f ( x )=x −7 x . Determine if this function is even, odd or neither. Explain/Show
work.

5. (2 pts each, no explanation required) The graph of the function y = f (x) is pictured below.

(a) State the domain of the
piecewise function.
(b) State the range of the piecewise
function.
(c) State the value of f (-3).

(d) State the interval(s) on which the function is increasing. That is, for what x-values is the
function increasing?
(e) List the local minimums, if any exist.
(f) The piecewise function has 4 pieces. Write the formula for just ONE PIECE of this piecewise
function. (You choose the piece you prefer. No explanation required)
f (x) = ___________________ for __________________ (state the x-values associated with your piece).
6a. Find the point-slope form of the line which passes through: P(-3,1) and Q(3,-5). (5 pts)

6b. Find the slope-intercept form of the line that passes through R(-6,-1) and S(2,-13). (5 pts)

7. In 2000, U.S. farmers received an average price of $157 per ton for shelled corn. In 2008,
they received an average price of 84.60 per ton.
a. What is the average rate of change in price of shelled corn over this time period? (3 pts)

b. Interpret the average rate of change in the context of this problem. (2 pts)

c. Find the linear function P(x) that models the change in the price of shelled corn over this time
period. (5 pts)

d. Based on your linear model form 7c, what is the predicted price of shelled corn for 2015?
(2pts)

8. Given the function f(x) =

f ( x) x 1 2

.

a. Sketch the graph of f. You may use the axis provided. (2 pts)

4
2
– – 24
4 22
4

b. State the domain and range in interval notation. (4 pts)
c. State the interval(s) where the function is decreasing. Use interval notation. (2 pts)
d. Find any absolute extrema. (2 pts)

9. A study was conducted by students in a Psychology class where they asked classmates to
study a list of nonsense words for various amounts of time and then to try to recall as many
words from the list as possible 30 minutes later. One student conducted the experiment with four

students. Their respective times studying the words (Time) and the number of words recalled 30
minutes later (Words) is displayed below.
Time
Words

3
7

5
8

8
14

10
18

The student graphed the data and thought that a linear equation would best model her data.
She then entered the data into a calculator and ran a Linear Regression on the data. A screen shot
of her results are below.

a. Based on this analysis, was she justified in using a linear model? Justify your answer using
the results above. (3 pts)
b. What is the slope of the regression line and interpret it in the context of her experiment. (3
pts)

c. Write the equation of the regression line. (3 pts)
d. Based on the regression line how many nonsense words would she expect someone to
remember if they were given 15 minutes to study? Show work to support your answer. (3 pts)

Bonus: A sales man gets a salary $1000 a month a 5% commission on all sales he makes that
month.
a. Write the equation S(x) that represents the salesman’s salary for any month. (3 pts)

b. If the salesman has a total of $30,650 in sales for this month, what would his monthly salary
be? (2 pts)

I have completed this exam myself, working independently and not
consulting anyone except the instructor. I have neither given nor
received help on this exam.
Name:

Date:

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