1. CME Mathematics II Chapter 4 Functions Objectives: Identify and describe patterns in tables Use differences to decide what type of function can fit a table Compare recursive and closed-form rules

2. Functions Work with your shoulder partner ◦Investigate Tables A through D on page 235 ◦For each table, find a rule that produces the given outputs. Discuss your rules within your groups and decide on one rule for each table

3. Functions

4. Functions Complete Table H Describe the function using your own words What is the Domain of the function?

5. Functions When you match a table with a rule, you are uncovering a hidden relationship in the numbers. Finding and describing the pattern can allow you to extend the domain to larger sets of numbers

6. Functions: Two Forms Closed form: A function definition such as… …is a closed form definition. This form lets you find any output g(n) for any input n by using direct calculation.

7. Functions: Two Forms Recursive form: A function definition such as… “ and output is 5 more than the previous output” is the recursive definition

8. Functions: Two Forms Recursive form: A recursive definition lets you calculate any output in terms of the previous outputs however you need a place to start. This is usually when n=0.

9. Functions: Difference Tables Difference Table: helps you find patterns that lead to recursive definitions To make a difference table, add a third column marked with the delta symbol Write the difference between one output and the next output in the third column

10. Functions: Difference Tables In this case the differences are all the same

11. Functions: Difference Tables In this case the differences are not the same Look at table D on page 241

12. For You to Do: #7 Show that the function d below fits Table D. Functions: Difference Tables