Question

Is there a mathematical function that is constant at 0, but once it hits 0, it begins increasing. I dont care what kind of increasing function it is: e, parabola, etc.
I am trying to avoid piecewise function.

Answer 1

The simplest is x + abs(x), though technically abs(x) is itself piecewise.

If you want something smoother, then try x^3 + abs(x^3), or any higher, odd exponent.

And another option that avoids using abs and is actually continuous: x + sqrt(x^2)