Domains of Compositions

Visualizing Compositions

Using graphical iteration to visualize the composition g(f) is straightforward. For any x in the domain of g(f),

1. draw the vertical segment from (x,0) to intersect the graph y = f(x) at the point (x,f(x)) 2. draw the horizontal segment from (x,f(x)) to intersect the diagoanal y = x at the point (f(x),f(x)) 3. draw the vertical segment from (f(x),f(x)) to intersect the graph y = g(x) at the point (f(x),g(f(x))) 4. draw the horizontal line from (f(x),g(f(x))) to intersect the vertical line through (x,0) at the point (x,g(f(x))).

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