Composite Functions

I love using Johnny Griffith’s Rich Starting Points with A-Level groups; they are self differentiating by outcome and any KS5 student can get something out of getting their teeth into them.

I recently used RISP 18 with a Y13 Further Maths group and it generated a lot of discussion and some nice algebraic proof. In about 45 minutes we worked as far as proving when two linear functions have the property fg(x) = gf(x) and what this tells us geometrically about their graphs but stopped short of the Mobius transformations! The photos below show what they produced on their “thinking” paper.



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