Project #1: Piecewise Function with Linear Pieces

This project requires that you use Desmos the free, online, web-based graphing. One of the best features of this site is that you can create, save, and share the things you create, provided you have a free account.

1. Choose data set to work with (see options below).
2. Select a section of data that can be modeled with a piecewise linear function that uses at least three pieces. You need not necessarily model the entire data set, but your sections should be adjacent and should contain at least 4 data points.

Part 1-Desmos Section:

1. Make a new Desmos graph and create a "note" text box. Type your name in the note text box.

1. Make several folders named "Piece 1," "Piece 2," etc. (use at least three pieces).

1. In each folder, create a table of at least 4 data points for that linear segment. Note:border values may be used twice (in adjacent tables, i.e. tables for pieces 1 & 2).

1. In each folder, write an equation for a line that appropriately models the data. You may work by hand or using regression.

1. Use inequalities to restrict the domains of each linear segment (ex:y=x+1 {0x

1. Save this graph as "Project 1-YourName." Note: You will turn this graph in with your project by posting a link on Canvas. To copy the link, click on the share graph icon.

Number of breweries in the U.S.

https://www.statista.com/chart/10280/americas-brewery-boom/

Project #1: Piecewise Function with Linear Pieces

Assignment Worksheet: Part 2 - Handwritten Section

1. Define/Explain your variables. Clearly state the meaning, and units, of both independent and dependent variables.

1. Write the function by hand in standard piecewise function notation, using your defined variables.

1. Discuss, compare/contrast slope of each piece. Write in complete sentences referencing the context of your problem. These should not be generic statements but should be meaningful in terms of the situation. The slope statements should make sense to someone who has not necessarily seen your data set.

1. Make at least five statements about the model in terms of the situation. Suggestions: consider discussing specific function values, intercepts, max/min points, increasing/decreasing/constant, domain/range, model breakdown, etc. a. Your observations should be fundamentally different from one another. For example is it fine to discuss a specific function value ( "f(2)=5 means that .....") but then your other statements should deal with other aspects of the function - not just repeat the same thing for a different input value. b. Your observations should be phrased as complete sentences that make sense to a reader who may not have seen your data set.