Linear Function Project
Project Description: Functions can be represented using equations, graphs, tables, and verbal descriptions. Over the course of this project, you will learn how to create and analyze functions in each of these forms.
For this project you will develop your own business. Your business can make/sell any school appropriate product or service that you would like. The relationship between your business's product or service and its cost must be represented by a linear relationship, meaning there must be a constant rate that the business charges. The following different parts of linear functions you will be applied to your own business:
Linear relationships
Independent and dependent variables
Constant rate of change
• Linear equations
• Domain and range of functions
• Representing linear equations with tables
• Linear functions- why is your business model an example of a linear function? Graphing linear functions and interpreting the meaning of different ordered pairs
• Comparing linear functions represented in different forms (tables, graphs, equations, written descriptions)
Constructing functions based upon graphs, tables, and written descriptions of linear relationships.
You will apply these concepts to your own business you will create a final presentation for your business. You may present your business in any way you would like (for example: posters, a power point, movie, etc), as long as it addresses each of the following questions and includes all of the vocabulary words listed above in the project description.
Questions you must answer:
1. What is your business?
a. The name
b. The product or service you sell. You may sell more than one thing, but you will need a separate equation for each product or service, and therefore will also need to address every required question for each product or service you
sell.
c. Why you want to sell this product or service.
d. You may also have a logo or any other creative addition you would like.
2. What are the independent and dependent variables in the linear relationship your business represents?
3. What is the constant rate of change/slope/constant of variation between the two variables in the linear relationship your business represents? 140w did you did you determine this?
4. Does your business have an initial fee or charge that must be included in your linear equation? If yes, what is this initial charge or fee? Where will it go in your linear equation?
5. What is the linear equation that represents your business? What form is this linear equation written in?
6. What are the domain and range of the linear relationship your business represents?
7. Create a table to represent the domain and range of your linear equation.
8. Explain why your business model is a function and create a function table.
9. Graph your function to display the profit your business will make. Pick at least one point off of your graph and describe what this ordered pair means for your business.
10. Compare your function to a real company that is similar to yours. Show this company's information in the form of a table, a graph, an equation, and in a written description. Compare this business to your business. Which business has the less expensive product?