# Representation of function by formula and table

Many of functions can be represented ( exactly or approximately ) by simple formulas. For example, the dependence between an area

*S* of a circle and its radius *r * is given by the formula *S* = *r*

^{2} ; the previous example shows the dependence between a height *h *

of a thrown body and a flying time *t *. But this formula is in fact an approximate one,

because it does not consider neither a resistance of air nor a weakening of Earth gravity by a height. It is very often impossible to

represent a functional dependence by a formula, or this formula is an uncomfortable for calculations. In these cases a function is

represented by a table or a graph.

E x a m p l e . The functional dependence between a pressure *p* and a temperature of water

boiling *
T* cannot be presented by the one formula, so it is

It is obvious, that any table cannot contain *all* values of argument, but an available for practice table must contain so many values,

that they are enough to work or to receive additional values by interpolating the existing ones.

### 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
- Designation of functions
- Functional dependence between two variables
- Constants and variables