imfreehand passing vertical line test

I am using the open imfreehand tool to make a one-to-one function: to draw a function curve along a 2d graph, but would like to set up limitations so that once an x value has been assigned a y value, no other y values for that x can be plotted. It does not need to be continuous (it can jump along the y axis)

I was currently toying with using a post-draw command that deletes those alternate points after the shape has been drawn, but I was wondering if there was a way to set up limitations within the imfreehand tool to do this. Thanks as always for your insight!