I am looking to construct a graph for illustrative purposes. I have a few restrictions that come from visualizing how the graph should look, in the form of $f(x,y) = z$.
$f(\infty,\infty) = \infty$
$0 < f(\infty,0) < \infty$
$f(0,\infty) = f(\infty,0)$
$f(0,0) = 0$
$f(-\infty,-\infty) = -\infty$
$f(\infty,-\infty) = -|f(\infty,0)|$
And for illustrative reasons, the negative-$x$ does not matter.
How would one go about approaching this?