eli5: Why does y=f(x+2) move it two units to the left (not right)?

Question

This is also the case where y=f(2x) where it dilates by a factor of 1/2. Why are they seemingly the opposite of what intuition tells me?

Edit:
Thanks guys 🙂 got it.

In: 0

Answer 1

Generally, for any given positive constant C, f(x+C) moves left by C units because the point that corresponds to f(0) is now at x = -C, which is clearly to the left. If C is negative, then it moves to the right because x = -C is positive.

Similarly, with scaling, it’s useful to see where f(1) ends up. For f(Sx) to equal f(1) (in the general sense), x = 1/S. For S > 1, 1/S < 1, so the point corresponding to f(1) is now closer to 0 than before, so it looks like a squish in with a high S.