1. Section 9.7 Functions

2. Function Definitions Def: A function is a rule that assigns one output to each allowable input. Def’s: The set of allowable inputs is called the domain of the function, and the set of possible outputs is called the range of the function.

3. Examples of Functions Ex 1: Doubling function- input: any counting number output: the number that is twice the input domain: ?? range: ??

4. Examples of Functions Ex 1: Doubling function- input: any counting number output: the number that is twice the input domain: the set of all counting numbers range: all even counting numbers Ex 2: The sequence shown below- input: any counting number output: the entry corresponding to that input number domain: all counting numbers range: the 3 different shapes in the sequence …. 1 2 3 4 5 6 7 8 9 10 11 12

5. Functions as Tables InputOutput 12 24 36 48 510 612 …… The Doubling Function City (input)Population (output) Lexington295,803 Louisville597,337 Nicholasville28,015 Frankfort25,527 Georgetown29,098 Population Function

6. Rules that aren’t functions

7. The Graphs of Functions Def: The graph of a function consists of all those points in a coordinate plane whose first coordinate is an allowable input and whose second coordinate is the output of the first coordinate. Ex: The doubling function: Each point is of the form (N, 2N)

8. The Graphs of Functions Ex 1: Draw the graph of the function given in the following table that shows how a rabbit population changes over time. Input: Time since 2005 (in years)Output: Number of rabbits 1200 2250 3325 4500 5800 6950 71000

9. See Activity 9FF

10. Functions as Expressions and Equations

11. Example Problem