Functional dependence between two variables
Functional dependence. Argument ( independent variable ).
Function. Singlevalued function. Multiplevalued function.
Two variables x and y are tied by a functional dependence, if for each value of one of them it is possible to receive by the certain
rule one or some values of another.
E x a m p l e . 
A temperature T of water boiling and atmosphere pressure p are tied by
a functional dependence, because each value of pressure corresponds
to a certain value of the temperature and inversely.
So, if p = 1 bar, then T = 100°C; if p = 0.5 bar, then T = 81.6°C. 
A variable, values of which are given, is called an argument or an independent variable; the other variable, values of which are
found by the certain rule is called a function. Usually an argument is marked as x, and a function is marked as y .
If only one value of function corresponds to each value of argument, this function is called a singlevalued function;
otherwise, if there are many corresponding values, this function is called a multiplevalued function ( twovalued, threevalued and etc.).
E x a m p l e . 
A body is thrown upwards; h is its height over a ground, t is the time, passed
from a throwing moment. h is a singlevalued function of t, but t is a
twovalued function of h, because the body is on the same height twice:
the first time at an assent, the second time at a fall. The formula
binding variables h and t ( initial velocity v_{0} and an acceleration of a gravity g
are constants here ), shows that we have only one value of h at the given t ,
and two values of t at the given h ( they are determined by solving the
quadratic equation ). 
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