Function is one and most fundamental mathematical concepts, it is applied in all exact sciences. Function in a general view is a dependence of sizes: with change of some size x other size can change at.
To understand need of existence of function, review an example. Any physical formula expresses dependence of one parameter from another. So, communication between pressure of gas and its temperature at the constant volume is expressed by a formula: р = VT, i.e. pressure r is in direct dependence on temperature of T and is its linear function.
When writing at = f (x) means some idea of dependence, i.e. the variable at depends on a variable x under a certain law or the rule. This law is designated in function as f. At the same time the variable at can depend both on one, and on several sizes. For example, pressure of the based liquid r = ρgh depends on liquid density ρ, heights of a column of liquid h and on the size of acceleration of gravity of g.
Pay attention that by means of application of function for each permissible value x the unambiguous value turns out at. In other words, the concept of function expresses the idea of action which needs to be made over one size to receive another. In this regard in technical disciplines the function is defined as the device on which entrance moves x, and at the exit arises at. So, function allows to establish compliance between two sets in such a way that to each element of the first set there corresponds the only element of the second set. At the same time this compliance is expressed by a certain rule or the law. Functions in mathematics can be expressed in various ways. The most habitual is representation of function in the form of a formula: at =sinx, at the =2nd +3, etc. But there is also evident way of expression of function – in the form of the schedule, for example, dependence of inflation on money supply. Some functions are presented in the table form. This way is unique in case the dependence is established experimentally, at the same time the formula is not removed yet, and the schedule is not constructed.