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It is possible for a graphing utility/calculator to plot a function incorrectly...

What are some possible errors that may occur?

What will cause those errors?

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You can construct a numerically unstable function like this:

y = (sqrt(x² + 9) - 3) / x²

which then goes wrong if you try and plot it near zero using regular floating point arithmetic, eg

http://www.wolframalpha.com/input/?i=y+%3D+%28sqrt%28x%C2%B2+%2B+9%29+-+3%29+%2F+x%C2%B2+from+-0.001+to+0.001

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  • $\begingroup$ Upvoted for the link illustrating the issue. $\endgroup$ – Jeppe Stig Nielsen Jan 3 '16 at 9:30

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