So, I am working with my son on transformations of functions.

He is ok with stretches and translations in the y direction but when we look at f(ax) or f(x+a) where the 'opposite' seems to happen to what he expects he gets lost! Anyone got a good way of thinking about this that can help him understand what is happening and why?

What is the best function to pick? I realised f(x) = x^2 is confusing!