9709 Pure 1 · 1.2 Functions · Sessions 4 and 5
Every change to a graph is a translation, a stretch or a reflection. Explore lets you set all four numbers in y = a f(b(x + c)) + d, watch each marked point travel, and read the description the way Cambridge marks it. Order matters does two moves in both orders so you can see when the answer changes.
Describe it fully
Where the marked points went
Pick two moves. The left graph does A, then B. The right graph does B, then A. Before you look at the verdict, decide whether the two final curves will match.
The rule underneath. A move outside the bracket acts on y. A move inside acts on x. Moves that act on different letters never interfere, so their order is free. Two translations just add, and two stretches or reflections just multiply, so those pairs are free too.
Where the order bites. A translation and a stretch or reflection that act on the same letter. Whichever comes second also acts on the first one's result. In an exam, a sequence is marked in the order you write it.