QUIZ 2 resubmit_240202_183151504
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Michigan State University *
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117
Subject
Mathematics
Date
Apr 3, 2024
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8
Uploaded by CaptainDuck1150
LB 117 – Spring 2024 – Quiz 2 (Sec 1.2-1.5, 2.1-2.4) 100 pts
Due Friday, 2/2/24 This quiz is due on Friday, 2/2/2024 by 11:59 pm in Gradescope
. Make sure to leave enough time to submit your quiz before 11:59 pm. If you have trouble uploading your work to Gradescope or if you want to be extra sure we receive your work, you can also upload your work into the D2L dropbox which is located under the Assessments tab and then the Assignments sub tab as an extra precaution. (Work will be graded in Gradescope, so please let the instructor know if you have Trouble submitting to Gradescope and she will submit your work to Gradescope from the file you submit to the dropbox on D2L.) The dropbox is only an extra precaution to make sure we receive your work by the deadline.
Please SHOW ALL YOUR WORK neatly on separate paper or electronically on a tablet or computer. No work = no credit. Points are not based on just your answers. The correct work is worth more than the final answer! No decimals allowed. EXACT ANSWERS ONLY.
After taking your quiz, scan and upload it in PDF form
to GRADESCOPE (and if you want to, theD2L dropbox for that particular quiz). There is a how to video under the WEDNESDAY QUIZ FOLDER that shows you some ways to scan your work and turn it into PDF form so it can be uploaded. I recommend the GRADESCOPE MOBILE APP.
If you have any issues with uploading your quiz, text me at 734-735-8311 RIGHT AWAY. No late quizzes will be accepted. Contact me before 11:59 pm if you have trouble submitting. -Hanni
In 2010, you have 300 songs in your favorite iTunes playlist. In 2013, you have 250 songs. In 2019, you have 571. What is the average rate of change per year in the number of songs in your favorite iTunes playlist between 2010 and 2019? Round to the nearest whole number QUESTION 2 4 points
Using the following figure, find the average rate of change of f for 1<x<2. QUESTION 3 4 points Suppose there are 700 people living in a small town and the rate of change of the town's population is 30 people per year. How many people will be living in the town fifteen years from now? QUESTION 1 4 points
QUESTION 4 6 points Find the coordinates of the x and y intercepts and the slope of the line 6x+24y=60 QUESTION 5 4 points Could the following table represent a LINEAR
function? Answer yes or no and give a reason for your answer. x
1 2 3 4 5 9 12 15 18 21 QUESTION 6 5 points Write the equation of a line with a slope of -4 which passes through the point (-1, 5).
QUESTION 7 5 points Suppose that f(x) is linear and that f(-2)=-10 and f(4)=14. Write the equation of the line through these points.
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QUESTION 8 4 points If a linear population function is 18,000 in year t = 0 and grows by 2,000 people per year, find a formula for P(t), the population as a function of time. QUESTION 9 6 points (3 pts each part) a)
What is the equation of a vertical line through the point (3, 6)? b)
What is the slope of any horizontal line? QUESTION 10 4 points Are the lines represented by these equations parallel? Perpendicular? Or neither? 5x+y=7 and y=-5x-7 Explain. QUESTION 11 3 points Are the lines represented by these equations parallel? Perpendicular? Or neither? y=-3x+2 and y=-1/3x-1/2 Explain. QUESTION 12 4 points Write the equation of a line that passes through the point (9, 8), and is perpendicular to y=6-3x.
QUESTION 13
15 pts
total
(part a = 7 pts, part b = 4 pts, part c = 4 pts)
a)
Graph the following piecewise function on the graph paper provided. Make sure to use open or closed circles appropriately and plot points carefully. 𝑓𝑓
(
𝑥𝑥
) =
�
𝑥𝑥
+ 3,
𝑥𝑥
<
−
1
2, −
1
≤ 𝑥𝑥
< 1
3
− 𝑥𝑥
,
𝑥𝑥 ≥
1
b)
Use the graph to give the DOMAIN of the function in INTERVAL NOTATION: c)
Use the graph to give the RANGE of the function in INTERVAL NOTATION:
QUESTION 14
9 points Write a formula for the following piecewise function: . QUESTION 15
6 points (2 pts each part)
Given the piecewise function: a) Evaluate f(6). b) Evaluate f(-4). c) Evaluate f(0).
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QUESTION 16 4 points Assume that the graph of f(x)
contains the point (–6, 4). What is the corresponding point on the graph of g(x)= f(x-3)-9? Make sure to give the new coordinates and also explain how far and in which directions it shifted from the original point. QUESTION 17 4 points The graph of g(x) contains the point (-4, 2). Give a formula for h(x) in terms of g(x) that has shifted this point to the point (-1, 1).
QUESTION 18 9 points (part a=5pts, part b-c=2pts each based on part a answers) Use the table for f(x) shown here as a parent function to answer the questions below. If the answers are undefined, make sure to say DNE or UND. -2 -1 0 1 2 3 2 -1 -3 -2 a)
If g(x)= f(x-2)-1, create a NEW TABLE for g(x) by shifting the points in the table for f(x) appropriately. b)
Find g(-2) based on your answer from part a. c)
Find g(x)= -2 based on your answer from part a.