# Designation of functions

Let *y *be some function of variable * x*; moreover, it is not essential, how this function is given: by formula or by table or by any

other way. Only the fact of existence of this functional dependence is important. This fact is written as: *y* = *f *( *x *). The letter

*f* ( it is initial letter of Latin word “functio” – a function ) doesn’t mean any value, as well as letters **log**, **sin**, **tan** in the

functions *y *= log *x*, *y* = sin *x*, *y* = tan *x. *They say only about the certain functional

dependence *y* of *x*. The record *y* = *f* ( *x *) represents *any *functional

dependence. If two functional dependencies *y* of *x* and *z* of *t*

differ one from the other, then they are written using different letters, for

instance: *y* = *f* ( *x *) and *z* = *F* ( *t* ). If some

dependencies are the same, then they are written by the same letter *f *:* y* = *f* ( *x *) and *z* = *f* ( *t* ). If an

expression for functional dependence *y* = *f* ( * x *) is known, then it can be written using both of the designations

of function. For instance, *y *= sin *x* or *f *( *x* ) = sin *x*. Both shapes are

equivalent completely. Sometimes another form of functional dependence is used: *y* ( *x* ).

This means the same as *y* = *f* ( *x *).

### Related post:

- Graphical solving of inequalities
- Graphical solving of equations
- Elementary functions and their graphs
- Composite function
- Inverse function
- Basic notions and properties of functions
- Coordinates. Graphical representation of functions
- Representation of function by formula and table
- Functional dependence between two variables
- Constants and variables