I have a function
$$ f(x) = {1 \over 1 + e^{-k(x-0.5)}} $$
that plots a logistic curve that is symmetric around the point $0.5 / 0.5$.
$k$ defines the steepness of the curve.
I would now like to add another parameter (let's call it $c$) that stretches/condenses the curve on the y-axis while it stays symmetric around its midpoint $0.5 / 0.5$.
How/where would I add $c$ to this function?
0.5 / 0.5
, that should be typeset as $0.5/0.5.$ Similarly $k$ and $c.$ I.e, with dollar signs. $\qquad$ $\endgroup$