# 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.