I am looking for a $\Bbb{R}\to\Bbb{R}$ function $f$ with two plateaus of different heights and a valley.
The function has a minimum for $x=a$ and $f(a)=b$.
The first (the one for smaller $x$) plateau has height $d$ and the second plateau (the one for larger $x$) has height $c$, see this figure:
One constraint is that $c>b \land d>b$; no constraint is set on the relative heights of the plateaus: it can be $c\lt d$ (as in the previous figure) or $c\geq d$.
I had a look at Function to show 2 peaks with different magnitudes but it requires a periodic function while I do not need a periodic function.
I also had a look at camel hump with trigonometry and in particular at this answer https://math.stackexchange.com/a/229838/10799 but I was not able to find suitable $a$, $b$, $k1$ and $k2$ to get two humps.
$$f(x)=2.5-\frac{1}{x^2e^x+0.5}$$ In general: $$f(x)=a-\frac{k}{(x+m)^{b}e^{cx+n}+d}$$ With some parameters seems to do the trick