9 problems to solve. Please see attachment.

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MATH 107 QUIZ 3

NAME: _______________________________

April, 2019

Instructor: S. Sands

I have completed this assignment myself, working independently and not consulting anyone except the instructor.

INSTRUCTIONS

• 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 Sunday, April 14.

• Show work/explanation where indicated. Answers without any work may 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 pts) For each graph, is the graph symmetric with respect to the x-axis? y-axis? origin?

(No explanation required. Just answer Yes or No to each question.)

(a)

(b)

Symmetric with respect to the

Symmetric with respect to the

x-axis? ____

x-axis? ____

y-axis? ____

y-axis? ____

origin? ____

2. (6 pts) Let 𝑓(𝑥) = 2|𝑥| − 3.

origin? ____

(no explanation required)

(a) State the zero(s) of the function. ________

(b) Which of the following is true? 2. ______

A. f is an even function.

B. f is an odd function.

C. f is both even and odd.

D. f is neither even nor odd.

3. (6 pts) Which of the following equations does the graph represent? Show work or explanation.

3. ______

A.

1

𝑦=− 𝑥+ 6

3

B.

1

𝑦= 𝑥+ 6

3

C.

𝑦 = −3𝑥 + 6

D.

𝑦 = 3𝑥 + 6

4. (12 pts) Consider the points (–3, 1) and (6, 4).

(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, #4, with the line 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. (10 pts) A ball is thrown vertically upward with an initial velocity of 40 feet per second from the top of the

180-foot high tower of Pisa. The height h in feet at t seconds after the ball’s release is given by

h(t) = –16t2 + 40t + 180 feet for 0 t 4.5 seconds.

(a) What was the height of the ball 2 seconds after the ball’s release?

(b) What was the height of the ball 4 seconds after the ball’s release?

(c) Find and interpret (in a sentence) the average rate of change of h over the interval [2, 4]. Show work.

3. (16 pts) Lana wants to purchase custom-made bumper stickers to advertise her business. Two

websites offer different deals:

Website A: Pay a fixed design fee of $65.00, plus $0.30 per bumper sticker

or

Website B: Pay a fixed design fee of $36.50, plus $0.45 per bumper sticker

(a) State a linear function f (x) that is Website A’s total charge A for an order of x bumper stickers.

(b) State a linear function g(x) that is Website B’s total charge B for an order of x bumper stickers.

(c) Lana wants to purchase 240 custom-made bumper stickers, as cheaply as possible. At which website

should she place her order? Show work/explanation and state your answer.

(d) For what number of bumper stickers x is the total charge exactly the same for both websites? Write

an appropriate equation, show algebraic work to solve for the answer, and state the final result

carefully.

(e) (work not required to be shown for this part) Suppose we want to find out: For what number of

bumper stickers is Website A the better choice for Lana rather than Website B?

Which inequality should be solved? Choose (i) f (x) < g(x) or (ii) f (x) > g(x).

Choice: __________

Fill in the blanks:

Website A is the better choice for Lana if ____(choose less or more) than ______ (enter number) bumper

stickers are ordered.

7. (7 pts) A graph of y = f (x) follows. No formula for f is given.

Which graph (A, B, C, or D) represents the graph y = f (x + 1) − 2 ?

EXPLAIN YOUR CHOICE.

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

y = f(x) 4

4

2

2

-4

2

-2

4

-4

-4

-2

-2

-2

-4

-4

A. (below)

2

4

2

4

2

4

B. (below)

4

4

2

2

2

-2

4

-4

-2

-2

-2

-4

-4

C. (below)

-4

7. _______

D. (below)

4

4

2

2

2

-2

4

-4

-2

-2

-2

-4

-4

8. (20 pts, no explanation required) Consider the graph of the function y = f (x) pictured below.

(a) State the value of f (−2).

(b) State the x-intercept(s), if any.

(c) State the y-intercept(s), if any.

(d) State the domain of the function.

(e) State the range of the 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. (17 pts) Based on historical data retrieved from the

government agency NOAA, the following chart of

Washington, DC yearly average temperatures was prepared.

Average Temperature (degrees)

y = 0.0344x – 10.107

R² = 0.6242

Washington DC Avg Temp

62

60

58

56

54

52

50

1860

1880

1900

1920

1940

1960

1980

2000

2020

Year

For this data set, the line of best fit, the regression line, is y = 0.0344x – 10.107,

where x = year and y = average Washington, DC temperature, in degrees. The value of r2 is 0.6242.

(a) Use the regression line to estimate the average Washington, DC temperature in 1919, to the nearest tenth of

a degree. Show some work.

(b) Use the regression line to predict the average Washington, DC temperature in 2019, to the nearest tenth of a

degree. Show some work.

(c) In what year (to the nearest year) does the regression line predict an average Washington, DC temperature of

63.0 degrees? Show work, solving an appropriate equation.

(d) What is the slope of the regression line and what are the units of measurement? In a sentence, interpret what

the slope is telling us, in the context of this real-world application.

(e) What is the value of the correlation coefficient, r (rounded to 2 decimal places)? Also, interpret its value:

Looking at the graph and the size of r, do you judge the strength of the linear relationship to be very strong,

moderately strong, somewhat weak, or very weak?

…

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