6B - Functions
6B - Content video: Functions
This video covers the theory and an example of mathematical functions.
|
|
A function is a rule that assigns to each \(x\)-value a maximum of one \(y\)-value. That is, no two ordered pairs contain the same \(x\)-value. From our knowledge of relations, the only types that qualify as functions are:
|
|
The vertical line test:
The vertical line test can be used to determine if a relation is a function.
The vertical line test can be used to determine if a relation is a function.
|
|
Function notation:
A function is fully defined by a rule and a domain. We can fully define a function, \(f\), using the notation below
A function is fully defined by a rule and a domain. We can fully define a function, \(f\), using the notation below
\(f\): Domain \(\rightarrow\) Co-domain, \(f(x)=\) Rule
- \(f\) is the name of the function. Generally, lowercase letters (\(f,g,h,...\)) are used to name functions.
- The domain of the function must be specified. Generally, interval notation is used to specify the domain.
- The co-domain is the set of values that \(x\) is mapped to. For VCE Mathematical Methods the co-domain is always \(R\). It is important not to confuse the co-domain with the range; the range is simply a subset of the co-domain.
- The notation \(f(x)\) replaces "\(y=\)" when describing the rule.
Restricting the domain of a function:
It is possible to restrict the domain of a function. This is done by providing a domain that is different to the maximal domain.
It is possible to restrict the domain of a function. This is done by providing a domain that is different to the maximal domain.
|
|