i did the exercice by moving manually constant distance and copying the curves in the curve editor, i would like to know if there is a way to do it automatically.
I'm not exactly sure what you mean, but have a look at 'Curve Modifiers' in the Graph Editor. Particularly the cycle modifier.
And if you want to have a curve run off into infinity, look at the 'extrapolation'. Setting this to linear might be what you're talking about.
But I'll need more specifics about what you mean.