Assume that the original function is f(X) and the translation function is g(x).

If you translate one unit to the right to get gx,

Then let a point on gx be (x, y)

Then the point on the original fx is (x-a, y)

Bring this into fx's

g(x)=f(x-a)

This is why X is changed to x-a when translating to the right.

For translation up and down, in the same way, y is changed to y-a up and y is changed to y+a down.

My method is contrary to your memory formula, but when you remember to translate left and right, remember to add and subtract right, add and subtract up and down.