Function Notation

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

Like (3,-2).

(simply a relationship between two numbers)

Example: 'y is twice as big as x'

So if x = 3, then y = 6

(That is the relationship between the two numbers)

Function: is a specific kind of relation where every input has exactly one output.

Both tables are relations.

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BUT...

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One table is a function.

One table is NOT a function.

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Do you see which is NOT a function?

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Function Notation: a specific way to write a relation when it is a function. When you see a relation written in function notation you know right away that it is a function.

General Function Notation: f(x)

Said out loud: "f of x"

Example: y = 3x + 2 is a relation.

It is ALSO a function.

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

y = 2x - 1 is a function.

So it can be written in function notation.

f(x) = 2x - 1

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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).