Why the Function Explorer tool may give unexpected results
Limitations of the
Function Explorer tool.
Some graphs may look wrong
If you plot a graph where the function value changes very rapidly for small changes in x,
the graph may display values other than what we expect. For example, compare the two graphs below.
The left one is the graph of y = sin(3*x) and is consistent with our expectations of sine curves.
On the right however is the graph of y = sin(63*x). As you can see, the peaks vary when they should all be the same height.
Why does this happen?
The line drawn by the grapher is actually a series of points. The graph window is 412 pixels (points) wide.
For each of these points it calculates the value of the function and plots it at the appropriate y coordinate.
It then links these points together with short line segments if they are not adjacent.
When pixels don't fall exactly on the peaks of the function, information is lost.
If two successive pixels happen to fall on each side of a peak, it will miss the peak entirely:
This only becomes a problem when the function is changing very rapidly with x, and the function is periodic, since
only then does the eye see the erroneous pattern.
Experiment with it yourself
If you look at this chart you can see the effect yourself.
As you increase the value of a you can see this effect begin to appear as a gets larger.
Due to a bug in the Flash player, printing graphs with inequalities does not work well. The shaded areas should be semi-transparent
but they print as solid colors. This makes them look too dark, and overlapping graphs cannot be seen properly. Once Adobe fixes this printing problem GFE should start operating correctly.
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