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[Ghandi10]

Hi I'm interested in finding out some graphs of the following function.

f(x) = 2x for 0 <= x < 0.5 and 2(1-x) for 0.5 <= x < 1.

In particular I would like to see some iterative plots of the function. Ie. f(f(x)), f(f(f(x)))) etc. If anyone knows where I can find some or if there is a way to compute them by hand could they please inform me? If anyone knows the general behaviour of the iteratives of f(x) that would also be good.

Ghandi

 

[Slidey]

One easy way to do it is draw a graph of f(x), then use your 4u graphing skills to draw f(f(x)) and so on. Let me try.

 

[acmilan]

If you get gnuplot, you can define as much composite functions as you want and graph them all together.

 

[Slidey]

As you can see the maximum point simply doubles each iteration and you simply draw a line between it and the points (0,0) and (0,1).

For the nth iteration, the maximum point will be ( 1/2 , 2^(n-1) ).

 

[§eraphim]

you could translate the graph to the left and do the calculation directly without looking at any graph.

 

[Templar]

If you want to find the results of repeat iterations on a particular point you can just draw y=x on the same graph and use that.