How to train a neural network to recognize graphs?

Question

Neural networks

Hello.
I have the task of recognizing the types of custom graphs (sinusoid, hyperbola, etc.), approximately.
I'm going to use the backpropagation method on a multilayer perceptron.
For training, I decided to use only standard graphs built according to formulas.
For example sinusoid a*Sin(x) + b. And I will provide a large number of examples by changing a and b.
Tell me, am I moving in the right direction or am I wrong in something?

Answer 1

in the correct
only not standard graphs, but graphs of standard functions

Answer 2

Is it not possible to immediately calculate the optimal coefficients for various types of functions, if they are rigidly specified? Do it in one step instead of going down the gradient.