I take no credit for this ‘aide-memoire’ – it comes from a most delightful and hardworking student. To quote a colleague “She is the poster-child for the benefits hard work”.

Let’s call this student Natasha (not even close to her real name). Natasha had been struggling to work out the difference between graph/function transformations, in particular f(x+a) and f(x)+a. Which way did the graph move? How could you tell? Then she had a brain wave:

She drew little Y shapes on the brackets:

One of the brackets now looks like a little crab:

And we all know crabs move sideways – so it most be a horizontal translation!

Simple!

Logical!

Genius!

Thank you Natasha!