Function

What is a function

A Function is

a relation is where each input is related to exactly one output

Functions In Tables

• For each input there is exactly one output

• Looking at a table all of the "x's" should be different

• If the x's are different it is a function

• If the x's are the same it is not a function

Functions In Tables

• For each input there is exactly one output

• Looking at a table all of the "x's" should be different

• If the x's are different it is a function

• If the x's are the same it is not a function

Functions In Ordered Pairs

• For each input there is exactly one output

• Looking at "x" all should be different

• If the x's are different it is a function

• If the x's are the same it is not a function

Functions In Mapping Diagrams

• For each input there is exactly one output

• If the x's are different it is a function

• If the x's are the same it is not a function

Functions In Mapping Diagrams

• For each input there is exactly one output

• If the x's EACH have ONE LINE

• If the x's have 2 or more lines it is not a function

Relation: a set of input and output values, usually represented in ordered pairs.

Like (3,-2).

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(simply a relationship between two numbers)

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Example: 'y is twice as big as x'

So if x = 3, then y = 6

(That is the relationship between the two numbers)

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FUNCTION

a specific kind of relationship where every input has exactly one output.

Function Notation

a specific way to write a relation when it is a function. ​

General Function Notation: f(x)

Said out loud: "f of x"

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Example:

y = 3x + 2 is a function.

So it can be written as f(x) = 3x + 2

Evaluating Functions

The questions we answered

Given y = 2x + 1, find the value of y when x = 5.

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Can be asked this way

Given f(x) = 2x + 1, find f(5).