Composition of Functions

Below, the purple point traces out the composition: g(f(x)).

Walk your way back and forth through it, and see why the result IS the composition.

The light blue diagonal line is the line y = x, which just simplifies the diagram a bit, since reflection off of it is the same as converting the output from f(x) into the input for g(x).

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Find the values: g(f(-3)), g(f(0)), g(f(4))

Dave Matthews, January 16, 2008, Created with GeoGebra