Lesson Extension: Patterns and Recursion

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Presentation transcript:

Lesson Extension: Patterns and Recursion Obj: The student will be able to identify and extend patterns using recursion HWK: p 646 2-14 even Vocab: 1) recursive pattern (recursive sequence)

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

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, ….

Ex 2) 1 8 , 1 2 , 2, 8, 32, …..

Ex 3) 1, 8, 27, 64, 125, ……

Ex 4) 56, 47, 38, 29, 20, …..

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

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.

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