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Weird Plot behavior...


I'm getting some strange, seemingly incorrect
graphs from Mathematica 3:

First I define a simple piecewise continuous
function:

sf[x_]:=If[x<(1/3),1-3 x,0.5 x - 1/6]

Then I graph its 4th iterate on [0,1] (along with
y=x):

Plot[{sf[sf[sf[sf[x]]]],x},{x,0,1}]

It's missing some information; in particular, the
graph only shows 5 fixed points when I know there
are 7.  And when I graph it on [0,2], I _do_ get
all 7 fixed points, and, yes, they're all on
[0,1]:

Plot[{sf[sf[sf[sf[x]]]],x},{x,0,2}]

What's going on?  Why is the first graph
incorrect, and the second correct?

Plot[{sf[sf[sf[sf[x]]]],x},{x,0,1},PlotDivision-
>5]

And here, even though I think I'm setting the
PlotDivision _lower_ than the default (20), I get
the right graph!

Doug


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