1. A Day at the County Fair Prepared by Gregorio Ponce, Ed. D. Imperial Valley Mathematics Project San Diego State University Imperial Valley Campus

2. Buying Tickets at the Fair Where is the function? People are using MONEY to purchase TICKETS .

3. What is the What is the Input Output ? ? The amount of money that I hand over determines how many tickets I get. Money Tickets

4. The Exchange: Money for Tickets 36 $45 24 $30 12 $15 Tickets Money

5. Can You See the Pattern? 48 60 36 45 24 30 12 15 Tickets Money

6. What’s the Function? The equation of this line is: y = .8x The function of the line is: f(x) = .8x The points make a pattern: A line This line has a slope : It is positive Two points helps us find the slope and the equation of the line. The equation of a line looks like this: y = mx + b

7. Are You Sure It’s a Function? A specific amount of money will buy me the same number of tickets each time. Money & Tickets In this example, the relationship between money and tickets follows a line. In other words: f(x) = .8x A function does something : The number of dollars times .8 gives the number of tickets. A Pattern A Condition Two Groups Function

8. How is a function useful? I can determine the number of tickets I would get for any given amount of money. 10 dollars can buy me 8 tickets x = 10 .8(10) y = 8 f(x) = .8x f(10) = .8(10) f(10) = 8

9. Key Question: How do functions help us uncover patterns in the relationship? Relationships become clearer when we look for patterns between two things. We can uncover these relationships by looking for patterns in numbers to help us create graphs which help us develop equations . We can then generalize about those relationships using functions.