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