### Functions and graphs: Relations and functions

### Example 3: Colour models

Also in computer science applications you may encounter many mathematical relation between quantities. The following example of a **linear relation** between four variables originates from conversion of colour models.

The relation between the gamma-corrected Luma signal \(Y'\) (perceived brightness) for HDTV and the gamma-corrected RGB signals \(R\,',G\,',B\,'\) is according to the BT.709 standard equal to

\(Y'=0.2125R\,'+0.7154G\,'+0.0721B\,'\)

In the above specific formula we call \(R'\), \(G'\) and \(B'\) **independent variables,** because each is a variable whose value can be freely chosen. The signal \(Y'\) is the **dependent variable,** because its value depends on the values of the independent variables. The Calculus module is limited to functions of one variable; functions of two or more variables are discussed in the Advanced Calculus module