Hi,
I can guess what this is for.
it's a common adjustment on RC controllers, it increases or decreases sensitivity around the throttle and steering centre points. It looks like a simple function that but my maths is way to rusty to attempt a definition.
A naive implementation would be to use a sine function with an offset, if you move the offset forwrd, you get the r shaped curve, if you move it back, you get the j shaped part of the curve. I am certain there is a better method but this might help other grasp what you are after, unless I am mistaken.
Duane B