Your own function

(z+3)*(z-3)/(z - mouse)

Root and pole

This is a graph of $f(z) = (w-z)/z$. Your mouse position is the $w$.

(mouse-z)/z

Zoom and pan

This is a graph of $f(z) = z^2 + z + 1$. You can use the scroll wheel to zoom, and drag to pan, but I believe this is broken at the moment.

z^2 + z + 1