is
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 of
Functions
have the following properties:
A Level Maths Notes: C3 – Functions
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, if
then
This
expression may be simplified, but still represents the same function.
Examples of functions
ofinclude:
Notice that a function may
be labelled by
Ifis
not present in the notation then it is understood that the variable
is
If the graph of
againstis
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