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

You’re basically just asking the question “What value would this function be at [position] rather than x, but show this value here”.

So f(x+2) asks “what is the value at thevposition 2 more than x, please show it at x”. That by definition takes a value from the right of x and moves it left from x+2 to x. The function shifts to the left.

F(2x) is same principle, but you’re asking “what’s the value at twice the value of x, show it here”, but everything positive moves left, everything negative moves right. The function squishes.

Same principle in the case of reverse operations, just reverse the result.