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Why Graphing Tools doesn't represent hole in a graph

  1. Dec 20, 2014 #1
    Why Graphing Tools doesn't represent hole in a graph of a function. A Hole at a point in a graph is point where function is not defined.Suppose there is a function

    ##\frac{x}{\root{x-1}-1}##

    Its should be like this
    Capture.jpg

    But online tools and even my android graphing tool app shows graph like this
    Capture_2.jpg

    What I'm saying is that, apart from circle there must be some sort of marks representing that the function is not defined here.
     
  2. jcsd
  3. Dec 20, 2014 #2
    What's your function? Plotting ## \frac{x}{\sqrt{x-1}-1} ## gives me a different graph.

    Anyhow, point discontinuities aren't always shown on generated graphics, but you can force the tool to do it.

    For example, take the function ## \frac{x^2-5x+6}{x-2} ## which has a point discontinuity at ##x=2##.

    Using WolframAlpha:

    >> plot (x^2-5x+6)/(x-2)gives this:
    MSP10311g15fe9bg4f36dc700000f418id2faei64h0.gif

    >>plot discontinuities of (x^2-5x+6)/(x-2) gives this:
    MSP42992072699fi0ig0dci000031436gf7gf8gd36b.gif

    Now, as for why these graphic tools don't show where point-discontinuities are? I don't know, I guess you have to ask for it, because we usually don't need to see it shown that big. Theoretically, the exact point ##x=2## in our example is so small if it were to be shown it would be unnoticeable. Note that the function behaves at ##x=1.9999999...## exactly how it does right after ##x=2##. The circle of point-discontinuity is just a symbol showing that something is going on here; it's not a real hole because point-discontinuties are actually impossible to show.
     
    Last edited: Dec 20, 2014
  4. Dec 20, 2014 #3
    About online graphing websites [for example Desmos]:
    I think that because the program is trying to show that the function is continuous on a very close interval beside the point where the function has a discontinuity, but if you click on that point it will give you its coordinate and whether it is defined or not. Untitled23.png
     
  5. Dec 20, 2014 #4
    Sorry mistyped the function ##\frac{x}{\root{x+1}-1}##
     
  6. Dec 20, 2014 #5

    Mark44

    Staff: Mentor

    \root{} doesn't mean anything in LaTeX. Use \sqrt{} for a square root and \sqrt[3]{} for a cube root and similar for higher-degree roots.

    Your expression should be written as # #\frac{x}{\sqrt{x+1}-1}# # (without the spaces between the # characters). This renders as ##\frac{x}{\sqrt{x+1}-1}##
     
  7. Dec 20, 2014 #6
    Hmm Sorry little mistake
     
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