Can you expand upon this? Perhaps the difference between "re-mapping" the function:

    f(x_1)=y_2

and "re-mapping" the value:

    x=42+2

How is the former different than the latter? And by what mechanism is the former achieved? I understand what you are saying, but how does one simply "change this same function"? Redefine it?

To be clear, I'm not suggesting you are incorrect. I just don't fully understand what you are getting at.