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.

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Presentation transcript:

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 …

Functions as Tables InputOutput …… The Doubling Function City (input)Population (output) Lexington295,803 Louisville597,337 Nicholasville28,015 Frankfort25,527 Georgetown29,098 Population Function

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

See Activity 9FF

Functions as Expressions and Equations

Example Problem