1. Lesson Extension: Patterns and Recursion
Obj: The student will be able to identify and extend patterns using recursion HWK: p even Vocab: 1) recursive pattern (recursive sequence)

2. 4 types of Patterns Using Recursive Techniques to Identify Patterns
Type of pattern
Characteristics
Linear
First differences are constant
Quadratic
Second differences are constant
Cubic
Third differences are constant
Exponential
Ratios between successive terms are constant

3. Identify the type of pattern
Identify the type of pattern. Find the next three numbers in the pattern.
Ex 1) 4, 6, 10, 16, 24, ….

4. Ex 2) 1 8 , 1 2 , 2, 8, 32, …..

5. Ex 3) 1, 8, 27, 64, 125, ……

6. Ex 4) 56, 47, 38, 29, 20, …..

7. To determine if a function is linear, quadratic, cubic, or exponential: (must make sure there is a constant change in the x-values first)
Using Recursive Techniques to Identify Functions
Type of function
Characteristics (given a constant change in x-value)
Linear
First differences of y-values are constant
Quadratic
Second differences of y-values are constant
Cubic
Third differences of y-values are constant
Exponential
Ratios between successive y-values are constatn

8. Ex 5) The ordered pairs {(-4,-4), (0,0), (4,4), (8,32), (12, 108)} satisfy a function. Determine whether the function is linear, quadratic, cubic or exponential. Then find three additional ordered pairs that satisfy the function.

9. Ex 6) Several ordered pairs that satisfy a function are given
Ex 6) Several ordered pairs that satisfy a function are given. Determine whether the function is linear, quadratic, cubic or exponential. Find three additional ordered pairs that satisfy the function. x y 1 3 2 9 19 4 33