Unit 7 Portfolio

x / y
1 / 8
2 / 35
3 / 62
4 / 89

Larry, Moe, and Curly spend their free time doing community service projects. They would like to get more people involved. They began by observing the number of people who show up to the town cleanup activities each day. The data from their observations is recorded in the given table for the Great Four Day Cleanup.

  1. Using complete sentences, describe what the domain and range in the table represent.

The domain (x) represents the number of days the activities are going on. The range (Y) shows how many people are showing up.

  1. Sketch the data on the grid below. Be sure to label and number each axis.


1 2 3 4 5 6

days

  1. What type of function is modeled in the graph? How do you know?
  1. Describe key features of the graph.
  1. Write an equation that models the function.
  1. Use the equation to predict the number of people who would help if the cleanup campaign went on for 31 days? You must show your work.

Excited about the growing number of people participating in community service, Larry, Curly, and Moe decide to have a fundraiser to plant flowers and trees in the parks that were cleaned during the Great Four Day cleanup. It will cost them $7,500 to plant the trees and flowers. To fund this project, they decide to sell pies for $6. For every 100 pies sold, they pay $25.00 for supplies and ingredients.

  1. Complete each table below to find the total number of pies sold and the money collected on Day 1 and Day 2.

Day 1 / Day 2
Customer Number / Number of Pies Sold / Amount Collected / Customer Number / Number of Pies Sold / Amount Collected
1 / 1 / $6 / 1 / 1 / $6
2 / 2 / $12 / 2 / 2 / $12
3 / 3
4 / 4
5 / 5
6 / 6
7 / 7
8 / 8
9 / 9
10 / 10
On Day 1, each customer buys the same number of pies as his customer number. / On Day 2, each customer buys twice as many pies as the customer before him.
  1. Using complete sentences compare the rates of change between Day 1 and Day 2 for the number of pies sold.
  1. What type of function does each day represent? Explain your reasoning.
  1. Write a function representing Day 1.
  1. Write a function representing Day 2.
  1. Did Larry, Curly, and Moe earn enough in two days to fund their project? You mustjustify your response. Consider the money earned as well as the cost of baking pies.

Rubric

Needs Improvement / Fair / Good
Question 1 / 0
Described the domain and range inaccurately or not at all / 1
Described either the domain or range accurately, or did not use complete sentences / 2
Described both the domain and range accurately using complete sentences
Question 2 / 0
Sketched none of the data accurately and labeled axes inappropriately or not at all / 1
Sketched some of the data accurately and labeled axes appropriately / 2
Sketched all of the data accurately and labeled axes appropriately
Question 3 / 0
Incorrectly identified the function and did not justify / 1
Incorrectly identified the function or did not accurately justify it / 2
Correctly identified the function and accurately justified it
Question 4 / 0
No key features of the graph were properly identified / 1
Some key features of the graph were properly identified / 2
All key features of the graph
Question 5 / 0
The equation was incorrect. / 1
Part of the equation was correct. / 2
The entire equation was correct.
Question 6 / 0
No work was shown / 1
An incorrect answer was given due to arithmetic errors in the work shown / 2
The correct answer was given, with work shown
Question 7 / 0-1
Some or none of the table was completed correctly / 2-3
Most of the table was completed correctly / 4
The entire table was completed correctly
Question 8 / 0
The rate of change was not correctly identified or described / 2
The rate of change for one day was correctly identified and described / 4
The rates of change for both days were correctly identified and described
Question 9 / 0
Neither function was correctly identified or a supporting response was missing or inaccurate / 1
The function for one day was correctly identified with an accurate supporting response. / 2
The function for both days was correctly written with an accurate supporting response
Question 10 / 0
The function was incorrect. / 1
Part of the function was correct. / 2
The entire function was correct.
Question 11 / 0
The equation was incorrect. / 1
Part of the equation was correct. / 2
The entire equation was correct.
Question 12 / 0-6
The response was inaccurate, not thought out or demonstrated little to no understanding of functions / 7-13
The response was somewhat accurate, well-thought out, and demonstrates a moderate understanding of functions / 14
The response was accurate, well-thought out, and demonstrates a complete understanding of functions