## Formulae

A function of is any formula with alone in it as a variable, so that a value may be chosen for and the value of the function calculated for this value of Functions have the following properties:

For a given value of there 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 of called 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, if then This expression may be simplified, but still represents the same function.

Examples of functions of include: Notice that a function may be labelled by If is not present in the notation then it is understood that the variable is If the graph of against is shown then the domain and range of the function may be read off the graph. The diagram shows the graph of The domain is and the range is  The diagram shows the graph of The domain is and the range is  