Attached is a Hype project:
AnimationIssue_v2.hype.zip (25.0 KB)
I am not certain if I got things right for You or not. In the attached screenshot I am showing the graph that I believed needed the work. However, it was identified as "Image L to R" (though seemed to be a right to left movement intended) - but the other: "Image R to L" appeared to be performing correctly (even though in my mind the line is moving left to right, so I'm not sure of your frame of reference).
In any case, even if I twisted your meanings, there is now an example of a graph animating to the left and a graph animating to the right in the attached project.
Also please note that I removed the grouping from one of the green rectangles ("R to L"). I kept the other one grouped for comparison. These green rectangles do not need a mask, they can grow from "0" pixels to the full desired length using basically the same technique: as the green rectangle moves to the left, this movement is matched by the increase in width (which moves to the right). The overall effect is that the left side of the rectangle moves to the left, the right side stays stationary.
There is no need for a mask here as the rectangle is an homogenous field - there is no detail to distort (in contrast to an image). The rectangle is always the same appearance no matter its width whereas an image would be distorted going from 0 pixels to 250 pixels (or whatever). So with the line graph in this case we always want it to be 100% and need the mask. Think of the mask as the outer sleeve of a matchbox and the image as the inner box full of matches. We want the image (matches) to slide out of the mask (matchbox) at the actual (non-distorted) size.