Download Section 9.7 Functions

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 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
Functions as Tables
The Doubling Function
Population Function
Input
Output
1
2
City (input)
Population (output)
2
4
Lexington
295,803
3
6
Louisville
597,337
4
8
Nicholasville
28,015
5
10
Frankfort
25,527
6
12
Georgetown
29,098
…
…
Rules that aren’t functions
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)
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
950
7
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 𝑥)
• A variable that is used for the outputs is called the dependent
variable. (usually 𝑦)
• A function can usually be represented by the equation
𝑦 = (expression in 𝑥)
• Ex: The doubling function: 𝑦 = 2𝑥
Example Problem
• Ex 2: Graph the function 𝑦 = 𝑥 2 − 3𝑥 + 2. Determine the domain
and range of the function.