Why is this (image) function transformation not logical?

functions coordinate-systems transformation

Solution 1:

The photo should be toward $-250$ and not $250$ if this transformation is applied, it will be helpful to break this down into smaller transformations first simply consider $f(x+250,y)$ this is obviously towards $-250$ now when when we do $f(-(x+250),y)$ we get a flip and the image is still towards $-250$; Note that $f(-(x+250),y)=f(-x-250,y)$.

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