Before starting a research of behavior of function, it is necessary to define area of change of the considered sizes. Let's accept assumption that variables belong to a set of real numbers.
Instruction
1. Function is the variable depending on value of an argument. An argument - a variable independent. Limits of changes of an argument are called the area of permissible values (APV). The behavior of function is considered in ODZ borders because in these limits the dependence between two variables not chaotic, and submits to certain rules and can be written down in the form of mathematical expression.
2. Let's consider any functional dependence of F=φ (x) where φ - mathematical expression. Function can have points of intersection with axes of coordinates or with other functions.
3. In function points of intersection with abscissa axis the function becomes equal to zero: F(x)=0. Solve this equation. You receive coordinates of points of intersection of the set function with an axis OH. There will be so many such points how many will be equation roots on the set site of change of an argument.
4. With ordinate axis the value of an argument is equal in function points of intersection to zero. Therefore, the task turns into finding of value of function at x =0. Function points of intersection with an axis there will be so many OY how many will be values of the set function at a zero argument.
5. For finding of points of intersection of the set function with other function it is necessary to solve the system of the equations: F=φ(x)W=ψ (x). Here φ (x) — the expression describing the set function F, ψ (x) — the expression describing function W with which the set function needs to find points of intersection. It is obvious that in points of intersection both functions accept equal values at equal values of arguments. Two functions how many decisions at the system of the equations on the set site of changes of an argument will have so many general points.