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Exploring Functions Through Real-World Examples

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This educational piece illustrates various functions found in daily life using practical examples. It covers the sleep habits of armadillos, the growth of bamboo, pizza sales, typing speed, cell phone charges, and marathon running. Each example includes a two-variable equation to highlight the relationship between independent and dependent variables, reinforcing the concept of functions in mathematics. Through function tables and equations, readers will learn how to analyze and predict outcomes based on these functions, promoting a deeper understanding of mathematical relationships.

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Exploring Functions Through Real-World Examples

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  1. Functions

  2. Animals An armadillo sleeps 19 hours each day. Complete a function table and write an equation using two variables to show the relationship between the number of hours h an armadillo sleeps in d days.

  3. Answer

  4. Equation h= 19d

  5. Botanist A botanist discovers that a certain species of bamboo grows 4 inches each hour. A. Write an equation using two variables to show the relationship between the growth g in inches of this bamboo plant in h hours. B. Use your equation to explain how to find the growth in inches of this species of bamboo after 6 hours.

  6. Answers A. g = 4h B. 24 inches

  7. A pizza shop sells 25 pizzas each hour. At the same rate, find the number of pizza sold after 1, 2, 3, and 4 hours. Make a function table. Write an equation using two variables to show the relationship between the number of hours h and p the number of pizzas sold. Pizza

  8. Answers

  9. Equation p= 25 h

  10. Typing • Suppose you can type 60 words per minute. What is the total number of words typed after 5, 10, 15, and 20 minutes. • Make a function table. • Write an equation using two variables to show the relationship between the number of words typed w and m minutes.

  11. Function Table

  12. Equation w= 60m

  13. Cell Phones • Verizon charges a customer $40 for each month of service. • Write an equation using two variables to show the relationship between the total amount charged c after m months of service. • Use the equation to EXPLAIN how to find the total cost for 6 months of cell phone service.

  14. Answers c = 40m $240 – Substitute m with 6 in the equation c = 40m.

  15. Running • The average marathon running speed is 5.5 miles per hour. Find the number of miles run after 1, 2, 3, and 4 hours at this rate. • Make a function table to show the number of miles after 1, 2, 3, and 4 hours. • Write an equation using two variables to show the relationship between the number of miles m and the h hours.

  16. Function Table

  17. Equation m = 5.5h

  18. Exit Ticket 1. The function rule is only true if . . 2. How do you know if a relation is a function?

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