In points of intersection of function have equal values at identical value of an argument. To find points of intersection of functions — means to determine coordinates general for the crossed functions of points.
Instruction
1. In a general view the problem of finding of points of intersection of functions of one argument of Y=F (x) and Y =F ₁ (x) on the XOY plane comes down to the solution of the equation of Y = Y ₁ as in the general point of function have equal values. Values x, F(x) satisfying to equality = F ₁ (x), (if they exist) are abscissae of points of intersection of the set functions.
2. If functions are set by simple mathematical expression and depend on one argument x, then the problem of finding of points of intersection can be solved graphically. Construct function graphs. Define points of intersection with axes of coordinates (x =0, y=0). Set some more values of an argument, find the corresponding values of functions, add the received points on schedules. The more points it will be used for construction, the more precisely there will be a schedule.
3. If function graphs are crossed, determine by the drawing of coordinate of points of intersection. For check substitute these coordinates in formulas which set functions. If mathematical expressions are fair, points of intersection are found correctly. If function graphs are not crossed, try to change scale. Take a step between construction points more to define on what site of the numerical plane of the line of schedules approach. Then on the revealed site of crossing construct more detailed schedule with a small step for exact determination of coordinates of points of intersection.
4. If it is necessary to find points of intersection of functions not on the plane, and in three-dimensional space, it is necessary to consider functions of two variables: Z=F (x, y) and Z =F ₁ (x, y). For determination of coordinates of points of intersection of functions it is necessary to solve the system of the equations with two unknown x and y at Z = Z ₁.