Please tell me how you can transform the unimodal function in such a way that at the maximum point the value $y$ of the function (regardless of the initial value) is equal to $1$ or tends to $1$. Let me explain what I mean in the picture.
Let's impose an additional condition: we do not know anything about the position of the maximum, or about the structure of the function itself, but for calculations, you can, for example, take:
$f(x)=0.014e^{-(x-1)^2}$
My idea (my solution) is to multiply the function $f(x)$ by a large coefficient $k$ and pass it through the sigmoid, for example:
$F(x)=ArcTan(k \cdot f(x))$
Then the maximum of the new function $F(x)$, regardless of the value of the maximum of the original function $f(x)$, will always be approximately equal to $1$.
Are there any other options?