I need a function that will produce a graph similar to the one below.
This function is odd, symmetrical relatively to origin in III quarter. A is an asymptote (the top part is similar to hyper-tangent); B is the length of "dead zone" (straight line), where the function value is 0. By changing A and B params the user can control the look of the function, so they have to be included in equation somewhere.
Also it's interesting to know, is there some unified procedure for restoring the function by graph? Maybe some super-computer can do that? I can imagine the approximation by using NURBS methods or similar, but hardly imagine this using analytical way.