smooth

A continous function that is monotonically non-decreasing on the interval [0,1], and is surjective onto [0,1] (with the domain again being [0,1]). Moreover, it has a small derivative when t is around 0 or 1. This means that as a rate function, an observer appears a slow startup, a quick middle, and a slow end. The function likely wont throw errors if a value outside of [0,1] is provided, but the exact output is undefined.