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.
Each $x$-value is associated to exactly one $y$-value.
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:
Read: y equals f of x
- $y$ is the function value
- $f(x)$ is the function term
- $y=f(x)$ is the function equation
An example for a linear function would be:
$f:x\mapsto y$e.g. $f:x\mapsto 5x+3$