This video is quite long so you might want to watch it in two sittings, but it does explain clearly what higher GCSE students need to know about transformation of graphs. Thank you Ukmathsteacher!
Maths is fun has a good explanation of this with some nice interactive activities and questions. Bitesize activities are here.
If you are studying GCSE you need to be able to draw and recognise graphs of simple functions, both straight lines and curves. If you are at college your computer might have software on it such as Omnigraph. If you are at home you can download free open source software that does the same job, called “Graph”. You can read more about Graph and download it here. When you have downloaded it experiment with different functions and see what happens to the graph. To enter x² you have to use x^2.
Here are some ideas of functions to try.
y=x, y=2x, y=3x, y=4x etc
y=x+1, y=x+2, y=x+3 etc
y=-x, y=-2x, y=-3x etc
y=x-1, y=x-2, y=x-3 etc
y=x^2, y=x^2+1, y=x^2+2 etc
y=x^2+x, y=x^2 +2x, y=x^2 +3x etc
y=x^3, y=x^3 +1, y=x^3 +2 etc