Sequence returning elements with "?"'s -- yet commands typed correctly

tbrzezinski shared this question 4 years ago
Needs Answer

Hey gang,


In attached applet, my immediate goal is to plot any holes the graph of a rational function may have. My means of doing so are as follows:


rootsd = roots of denominator

rootsn = roots of numerator

commonroots = roots of BOTH numerator & denominator (for which graph of rational function will have a hole at these x-value(s))


I created a sequence called lines that has x = any number value from commonroots.

Then, when I created the holes list, I got points back with (?, ?) for coordinates.


In the example shown in attached file, the rational function has 2 holes (one at (-1, r(-1)) and (0, r(0)). Yet WHY am I getting this? I believe I typed in commands correctly.


Thank you in advance for any help you can provide.


Tim Brzezinski

Comments (3)

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Hi Tim,

(-1, r(-1)) and (0, r(0) are both undefined when I put them to test in desktop Geogebra.

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OH..... I'm sorry.....OF COURSE!!!! function r is undefined at those points. Sorry! I know how to fix it now. Thank you for pointing out the obvious.... :)

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A hole in GGB is undefined, because it's a hole.....

An approximation with the Midpoint of a segment over the hole.


  1. holes = Sequence[Midpoint[(Element[xvals, i], r(Element[xvals, i] + 10⁻¹⁵)), (Element[xvals, i], r(Element[xvals, i] - 10⁻¹⁵))], i, 1, numberofholes, 1]

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