how to map rectangular coordinate system onto JavaFX GraphicsContext canvas I am trying to figure out how to apply the proper sequence of translate and scale commands (or a single .transform command) so that the default pixel grid (0,0,1920,1080) for instance is setup so that the coordinate system  (minx,miny,maxx,maxy) can be used where for instance 
minx=100 maxx=200 miny=-5 maxy=5

I am trying to render mathematical functions and map the results to pixels and use the mouse to select certain regions to zoom in on.. my current code is at 

https://bitbucket.org/stephenc214/fastmath/src/default/src/fastmath/fx/HardyZMap.java

I would really appreciate any help... I know this is simple but I just can't seem to get it to work properly
You can map [x, y] pixel coordinates in an image of size [width, height] to your given range as follows:

x'=minx+(maxx-minx)*(x+0.5)/width;
y'=miny+(maxy-miny)*(y+0.5)/height;