I'm trying to create a slider that lets the user pick a value as low as some given minimum, or as high as some given maximum. The slider must also, when positioned half way, have a value that is some given "mid point".
So I'm looking for an increasing function $f(x) : [0,1] \to \mathbb{R}$ such that
$f(0)=k_{\mathrm{min}}$
$f(\frac{1}{2})=k_{\mathrm{mid}}$
$f(1)=k_{\mathrm{max}}$
for any $k_{\mathrm{max}} ≥ k_{\mathrm{mid}} ≥ k_{\mathrm{min}}$.
What could I choose? My first thought was a quadratic, since I have three unknowns, but this was non-inreasing for some values.
Thanks.