Math 124, Sections E and G: graphing calculator inaccuracies

(I made these plots on the computer in my office; you may be able to reproduce these effects on a graphing calculator or your home computer.)

Here are two plots, both of the function (sqrt(x2+9)-3)/x2. Zooming in on the point where x=0 (where there is a removable discontinuity in the graph) leads to the second plot.

It turns out that the first plot is more accurate, but without calculus (or some other tool), it's hard to decide. The corners and other features of the second graph come from inaccuracies in the computer's arithmetic.

Next, look at the function xex. My first plot came out looking like this:

A quick derivative calculation tells me that there is a critical point at x=-1, so I get more detail if I focus in on that:

I might have missed this minimum just using the computer: calculus told me where there was an interesting part of the graph, so it helped me focus my attention. (There is also an inflection point at x=-2, which is visible in the second graph but not the first.)

Finally, some calculators and computer programs won't plot this function correctly: f(x) = (x2-1)2/3. They may omit the parts of the graph where x < -1 or where x > 1, for instance. (Some will plot it correctly, though.)
Questions or comments? E-mail me at palmieri@math.washington.edu.

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Last modified: Mon Apr 29 12:59:28 PDT 2002