I come from a programming background and I can’t find a simple math function. The request might seem strange, but I needed it a graphical context to alter some points locations:
I need a function $f(x) = y$ defined for $x \ge 0$ such that:
- $f(x) \in [0, x)$
- $f(0) = 0$
- $f(x) \approx x$ as $x\to \infty$.
- It has to slowly grow at first — sort of like $x^2$ — and then get closer and closer to x.
The simplest equation form that satisfies this restrictions will do.
I tried to plot this so that I can make myself better understood:
Actual values don’t matter, just the shape of the plot.
None of the basic functions (and combinations of them) that I tried were doing this (e.g. $x^2, \log x, \sqrt x, 1/x$).