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# Domain and Range of a Function

## Discrete and continuous functions and dependent and independent values

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Nike
Teacher Contributed

## Real World Applications – Algebra I

### Topic

How much profit does Nike make off their shoes?

### Student Exploration

It’s rumored that it costs Nike about 5 to make each pair of shoes they make. 1. How can we interpret this sentence as a function, \begin{align*}f(x)\end{align*}? Let’s assume the input is the number of shoes Nike makes and the output is the total cost. 2. What’s the domain of this function? What’s the range? How do you know? 3. How would you graph this relationship? What are realistic values for the \begin{align*}x\end{align*}? What are realistic values for \begin{align*}y\end{align*}? 4. How many pairs of shoes did Nike sell in order for their net income to be549 million?
5. What is \begin{align*}f(100)\end{align*}? Interpret this into words.
6. What is \begin{align*}f(x) = 255,000\end{align*}? Interpret this into words.
7. Why is it important to be able to represent this relationship using functions?

The people that make Nike shoes in Vietnam make about \$10 for about 65 hours of work per week.

8. How can you interpret this sentence as a function, \begin{align*}g(x)\end{align*}? What would be the input, and why? What would the output, and why?
9. Graph this relationship on a set of axes. What are realistic values for \begin{align*}x\end{align*}? What are realistic values for \begin{align*}y\end{align*}? How are they different from your domain and range from the previous graph?
10. What is \begin{align*}g(20)\end{align*}? Interpret this into words.
11. What is \begin{align*}g(x) = 100\end{align*}? Interpret this into words.
12. Compare your functions, graphs and calculations from both relationships. What conclusions can you draw about the company?

### Resources Cited

http://www-personal.umich.edu/~lormand/poli/nike/nike101-4.htm

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