I would have thought based on the earlier section’s notation that moving a point to (-4,3) should correspond to t_-4,3, but here it’s written t_-3,4 and repeated. Can you clarify?

Then later in the section where you define G-function transforms, it seems that if you consider the one dimensional case where g = t_10, if you chose x = 0 at the origin, then gx = 10 and (g^-1)x = -10, so by your definition f’(0) = f(-10). But then this new f’ would be a right-shifted copy of f (i.e. each point in f’ would be 10 units to the right of its coordinate in f), while the section describes it as a left-shift. Can you clarify this?