Name ____________________________Quarter 4 Linear Functions ProjectMath 7/8, Spring 2020

We B Jammin'

Everyone loves a good tune or beat! So many people these days purchase songs digitally online from music companies. The purpose of this project is to investigate some of the music companies, and how much digital music actually costs.

Skills needed for success on this project: In depth knowledge of graphing linear functions, finding and interpreting slope, finding and interpreting x and y intercepts, domain and range in context, and solving equations.

Part 1: Tune Analysis

There are many online choices for purchasing digital tunes. The top 4 most popular choices these days (based on user friendliness and price) are iTunes, eMusic, Amazon MP3, and Napster. You decide that you are going to purchase music from these stores only for the next month. Below is an equation that represents each music company’s cost for 1 month of songs.

iTunes: f (x)=x eMusic: f (x)=1.50x

Amazon MP3: f (x)=0.50 x+10 Napster: f (x)=1.75x−20

Task 1: Interpretation of EquationsWrite a brief paragraph explaining what each equation means in relation to each company. Define your variables as x = # of songs, and y = f(x) = total cost of songs for the month.

iTunesf (x)=x

eMusicf (x)=1.50 x

Amazon MP3f (x)=0.50x+10

Napsterf (x)=1.75x−20

Name ____________________________Quarter 4 Linear Functions ProjectMath 7/8, Spring 2020

Task 2: Logical Thought and JustificationDo all four equations make sense for a situation involving purchasing t-shirts? ___________

Explain your answer.

Task 3: Table RepresentationMake a table of values for each digital music company, assuming you will buy at most 50 songs in one month. Be sure to label appropriately with variables and context!

iTunesf (x)=x

Number of Songs X Cost ($) Y

0 0 10 10

eMusicf (x)=1.50 x

Number of Songs X Cost ($) Y

0 0

Amazon MP3f (x)=0.50x+10

Number of Songs X Cost ($) Y

0

Napsterf (x)=1.75x−20

Number of Songs X Cost ($) Y

0

Name ____________________________Quarter 4 Linear Functions ProjectMath 7/8, Spring 2020

Task 4: Domain and Range in ContextWrite an appropriate domain and range for each music company.

iTunesf (x)=x

Domain:

Range:

eMusicf (x)=1.50 x

Domain:

Range:

Amazon MP3f (x)=0.50x+10

Domain:

Range:

Napsterf (x)=1.75x−20

Domain:

Range:

Task 5: Predicting and EstimatingWhich music company do you think has the best deal for 1 month? ____________________________________________

Explain your answer. _____________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________

_____________________________________________________________________________________________________________________

_____________________________________________________________________________________________________________________

Name ____________________________Quarter 4 Linear Functions ProjectMath 7/8, Spring 2020

Part 2: Graphical Music (SEE NEXT PAGE FOR BETTER GRID!)

Task 6: Graphing Linear FunctionsGraph each equation for the music companies on the same coordinate plane. Be sure to indicate which line represents which music company. Set appropriate intervals and label your graph.

Name ____________________________Quarter 4 Linear Functions ProjectMath 7/8, Spring 2020

X(# Songs)

Y(Cost $)

Name ____________________________Quarter 4 Linear Functions ProjectMath 7/8, Spring 2020

Part 3: Graphical InterpretationTask 7: Interpretation of SlopeExplain what the slope represents in each different music company equation.

iTunesy=x

The slope is ________ and it means…..

eMusicy=1.50 x

The slope is ________ and it means…..

Amazon MP3y=0.50x+10

The slope is ________ and it means…..

Napstery=1.75 x−20

The slope is ________ and it means…..

Task 8: Interpretation of Intercepts

Part A: Describe the differences in the x- intercepts for each graph. Describe in the context of this problem, how the x-intercepts pertain to the music companies’ cost and your music purchasing for 1 month.

Part B: Describe the differences in the y- intercepts for each graph. Describe in the context of this problem, how the y-intercepts pertain to the music companies’ cost and your music purchasing for 1 month.

Name ____________________________Quarter 4 Linear Functions ProjectMath 7/8, Spring 2020

Part 4: Computation using Linear Functions and Function Notation

Task 9: Function Notation and Computation

Part A: From which music company should you buy music from if you are going to purchase 25 songs in 1 month? Support your answer using information from your graph and/or equations.

Part B: You decide you will purchase at least 50 songs. Which company should you use? Support your answer using information from your graph and/or equations.

Part C: Happy Birthday! You get a $25 iTunes gift card How would that change the equation that represents your iTunes purchases for 1 month? Explain.

Name ____________________________Quarter 4 Linear Functions ProjectMath 7/8, Spring 2020

Part 5: Summarize and Reflect: Task 10: Now you will summarize and reflect on what you've accomplished with this project.

Part A: What skills did you need to use from math class in order to successfully complete this project?

Part B: What part of the project did you do the BEST on? Why? What part was the hardest for you? Why?

Part C: What did you learn from this project? Explain how math can be used in every day life.

Part D: Reflect on yourself. On a scale of 1 to 5, with 1 being "I did no work" and 5 being "I did my very best!” rate yourself and explain why you gave yourself that rating.

Part E: How would you improve this project?

*** Academic Integrity Statement:

I certify that this project is a product of my own work and effort: ________________________________________ (Electronic signature)