Section 9.7 Functions. Function Definitions Def: A function is a rule that assigns one output to...

Section 9.7 Functions

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.

Examples of Functions• Ex 1: Doubling function- input: any counting number

output: the number that is twice the input domain: ?? range: ??

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 numberoutput: the entry corresponding to that input numberdomain: all counting numbersrange: the 3 different shapes in the sequence

….

1 2 3 4 5 6 7 8 9 10 11 12

Functions as Tables

Input Output

1 2

2 4

3 6

4 8

5 10

6 12

… …

The Doubling Function

City (input) Population (output)

Lexington 295,803

Louisville 597,337

Nicholasville 28,015

Frankfort 25,527

Georgetown 29,098

Population Function

Rules that aren’t functions

The Graphs of FunctionsDef: 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)

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

1 200

2 250

3 325

4 500

5 800

6 9507 1000

See Activity 9FF

Functions as Expressions and Equations• A variable that is used for the inputs of a function is called the

independent variable. (usually )• A variable that is used for the outputs is called the dependent

variable. (usually )

• A function can usually be represented by the equation = (expression in)

• Ex: The doubling function:

Example Problem• Ex 2: Graph the function . Determine the domain and range of the

function.