Function Composition – Deeper Understanding

A simple twist on the typical exam question.  Do pupils appreciate that each point on a graph is an instance of (x, f(x)) ?  Do they realise that the composite function has coordinates (g(x), f(g(x)) ?

This graph could be presented to pupils.  Then have them select pairs of points to put in the table to notice the relationships and explore the underpinning principles of composition. 

Credit: @chrismcgrane84

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