How to determine if the coordinates belong to one of the graphs?

Question

Mathematics

Hello!
There is a charting program. Graphs are represented as a container with points (x,y) and are drawn as polygonal curves. There is a problem of definition of the schedule at induction of the pointer on it.
Can you please tell me in general terms how this can be done? The only thing that comes to mind is a banal enumeration of all graph values ​​when changing the position of the mouse cursor, but this is inefficient, since graphs can be more than 100,000 points.

Answer 1

Something I do not understand, what is the problem? Substitute x,y into the function and check if the equation is true, if yes, this coordinate belongs to the graph of the function.
y = x^2+2x-4
Point (3, 11)
11 = 3^2+2*3-4
11 = 11
Point (3, 11) belongs to the graph of the function y = x^2+2x-4.

Answer 2

If we are talking about the UI, the graphs are multi-colored and it is enough to find at least one of them at the intersection point of the graphs, then you can do the stupid thing, "look" at the color of the point under the pointer.