How to find the intersection point of two graphs?

Question

Mathematics

What are the options for finding the intersection point of two graphs (any), except for their equalization and construction, should there be another way?

Answer 1

The only way is to solve the equation by equating 2 functions for plots. Plotting is actually a graphical solution to this equation.
Further it will depend on how the schedules are set. If these are sets of points, then you need to find 2 identical points in sorted arrays. Or to cross a bunch of segments, if the graph is piecewise given.
If the graphs are given by functions, then you need to solve the equation. Numerical methods will help you here, if these are not polynomials of degree 4 or less. For example, Newton's method.
There are no other methods.

Answer 2

In the general case, the problem is difficult to solve, therefore it is equivalent to the problem "Find all the roots of an unknown equation", because in order to find the intersection of the graphs, you need to subtract their equations algebraically, thus obtaining a new equation, and then find the roots for the found equation.
Numerical methods for solving equations, as a rule, work well when the root exists and is unique - one of the simplest - half division, works if the root is unique and at the ends of the segment under study, where this root is located, the function has different signs.
Only for polynomials it is possible to build a procedure for finding all the roots automatically ( Lobachevsky-Greffe method ), but there may be nuances there too.