A happy afternoon spent analysing how functions move as you change coefficients. If I know the shape of f(x), what do I know about the shape of cf(ax + b) + d? Use Desmos to see things quickly (but maybe also skate over deeper thought as to why?)
I love a table to organise thoughts:
- Go beyond “if it is in the brackets then it is the opposite of what you would expect” to a deeper understanding of how the graph moves
- Tweak the activity to ensure that no graph can be drawn without deep thinking. An over-reliance on graphing software is a dangerous thing.