# Functions as relations

A relation is a set of ordered pairs. It assigns each element to at least one other element.

**Functions** are also relations, but only one assigned value may exist for each domain value.

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### Remember

A

Each $x$-value is associated to

**function**is an explicit relation $x\mapsto y$.Each $x$-value is associated to

**exactly one**$y$-value.## Notation

Functions are labeled with a letter. In most cases you use the letter $f$.

The $y$-value is assigned to the $x$-value. To show this dependency, one often writes:

$y=f(x)$

*Read: y equals f of x*

- $y$ is the
**function value** - $f(x)$ is the
**function term** - $y=f(x)$ is the
**function equation**

### Example

An example for a linear function would be:

$f(x)=5x+3$ or

$y=5x+3$

i

### Info

There is another notation for functional equations, which is less common in school:

$f:x\mapsto y$

e.g. $f:x\mapsto 5x+3$