Function specifies communication between elements of sets. Therefore to announce function it is necessary to specify the rule by which the element of one set called a set of definition of function is put in compliance the only element of other set – a set of values of function.
Instruction
1. Set function in the form of a formula, specify operations and their sequence of performance which need to be made from a variable as a result to receive value of function. This way of a task of function is called an obvious form. For example, ƒ (x)= (x³+1)²− √ (x). Range of definition of this function set [0; + ∞). It is possible to define function in such a way that at some values of an argument it is necessary to use one formula, and at other values of an argument – another. For example, function signum x: ƒ (x) =1, if x> 0, ƒ (x)=-1 at x <0 and ƒ (0)=0.
2. Work out F equation (x; y) =0 so that set of its decisions (x; y) was such is that for each number x in this set there is only one couple (x0; y0) with x0 element. Such form of a task of function is called implicit. For example, the equation of x×y+6=0 sets function. And the equation of a look x²+y²=1 sets compliance, but not function as among solutions of this equation there are two couples with a coinciding first element, for example, (√ (3)/2; 1/2) and (√ (3)/2;-1/2).
3. Express values of variables x and y through the third size which is called parameter, that is set function in the form of x=φ(t), y=ψ(t). Such type of the announcement of function is called parametrical. For example, x=cos(t), y=sin(t), t ∈ [-Π/2; Π/2].
4. For the best presentation set function in the form of the schedule. Determine the system of coordinates and in it represent a set of points with coordinates (x; y). Such way of the announcement of function does not allow to define precisely values of function, however is very frequent in the technician or the physicist there is no opportunity to set function in a different way.
5. If a set of values x of course, then announce function by means of the table. That is make the table in which to each value of element x the value of function of ƒ is put in compliance (x).
6. Express functional dependence in a verbal form if there is no opportunity to set function analytically. A classical example is the Dirikhle function: "Function is equal 1 if x – a rational number, function equally 0 if x – irrational number".