1. CME Mathematics II Objectives:
Chapter 4 Functions
Objectives:
Explore difference tables with a constant difference
Use Up & Over Property
Use Hockey Stick Property

2. Constant Differences Recall table H
In lesson 4.02 you saw that the recursively defined function below fits this table
Constant Differences

3. You can use a recursive definition that has constant differences to find a closed form that also fits the table.
Read Minds in Action pg
Therefore, if I want to know f(4), I need to know f(3), and f(2), so on…for a total of 4 steps.
Constant Differences

4. Functions: Two Properties
Up-and-Over Property: An output is the sum of the two numbers above it (the output directly above and the difference above and to the right)
Functions: Two Properties

5. Functions: Two Properties
Hockey Stick Property: An output is the sum of all the differences above it to the right and the single output at the top of the table
Functions: Two Properties

6. Functions: Theorems Theorem 4.1
You can match an input-output table with constant differences with a linear function. The slope of the graph of the function is the constant difference in the table.
Functions: Theorems

7. Functions: Theorems Theorem 4.2
If f(x) = ax+b is a linear function, then its differences are constant
Functions: Theorems

8. You can use the hockey stick property to quickly find a closed-form definition for a function that fits a table with constant differences.
Describe how you can find the number 23 using the hockey stick property
How can you use the hockey stick property to find a closed form that agrees with the table 3
Constant Differences

9. Constant Differences: Practice
Check Your Understanding pg.249
#1-3, 6,7 in class (worksheet)
Constant Differences: Practice