get curve out of mathematical functions

hey guys, i didn't find an answer yet to solve my problem.
i'd like to get two curves out of mathematical functions. actually, it's basically one curve; the other one is like the first but turned around 180° at one point.
as you can see on the pics i want to be able to move the upper surface back with a slider.
my conditions for now:

 -f(x) = g(-x) --> turned around at 180°

both curves must have one asymptote in common at one point (let's say it's 0;0)

the curves must have the same starting point and the same ending point (or at least two intersections)

the maximum of the upper curve must be left from 0

the curves mustn't change their length inbetween the two intersections as a real surface can't shrink either

in general my question is the following: is it even possible to create real curves out of mathematical functions and loft (or sweep) them to get surfaces? in the end i'd like to have one slider to move the whole surface like i do in the pictures.
gh-pros, please help!

thx a lot in advance

pryz.