Odd root like function, but with asymptotes

Question

I have the following function:

$\frac{1}{2}\left(-x\right)^{\frac{1}{1+2\cdot d}}+\frac{1}{2}$

Where d is an integer, ensuring that (-(x+f)) is taken to an odd root. I'm using the function as part of a machine learning algorithm; the key feature I need is the sudden drop in values at a certain point, but instead of the outputs of the function becoming negative as x increases, I need it to approach a horizontal asymptote at 0 and 1.

Is there any function that might satisfy those requirements?

Answer 1

The closest I could find was inverse tangent:

$tan^{-1}(x)$

Though it hasn't been transformed to fit the original question's needs.