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Osc89 said:
It's to do with the absolute value of A, not whether it is positive or negative. I think it is a property of homogeneous functions, as -f(Ax) = f(-Ax), so it has to have that kind of symmetry


I see, It's just strange that horizontal stretches are based on absolute value rather than positive or negative, while vertical stretches, vertical shifts, and horizontal shifts are completely different. 

Never heard of homogeneous functions. Should I have?