## Formulae

A function ofis any formula withalone in it as a variable, so that a value may be chosen for and the value of the function calculated for this value ofFunctions have the following properties:

For a given value ofthere is only one value of a function

A function may have one value for different values of

A function may be defined for only certain values ofcalled the domain.

The set of all values that a function may take is called the range or codomain of the function.

For every function we may plot elements of the domain against elements of the codomain ie points

A function is defined entirely by it's form. For example, ifthen This expression may be simplified, but still represents the same function.

Examples of functions ofinclude:

Notice that a function may be labelled byIfis not present in the notation then it is understood that the variable is

If the graph ofagainstis shown then the domain and range of the function may be read off the graph.

The diagram shows the graph ofThe domain isand the range is

The diagram shows the graph ofThe domain isand the range is