I'm trying to create a function for a research project, but I fear my math knowledge is insufficient to derive it from the attached diagram I've created showing its desired behavior. I'm hoping someone will recognize the behavior and provide some leads on similar functions to lead me in the right direction.
For the axes we have $X \in [0,1]$ and $Y \in (0, \infty)$. The dotted lines are isometric lines of the Z axis. The Z values and exact shape of the isolines are not as important as the monotonicity of the graph w.r.t. both X and Y. I'm not against having a piecewise function for $Y>1$, $Y=1$, and $Y<1$ if necessary but a single function would be a bonus.