Why Graphing Tools doesn't represent hole in a graph

  • #1
142
1

Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
77
9
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:
  • #3
105
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
 
  • #4
142
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.
Sorry mistyped the function ##\frac{x}{\root{x+1}-1}##
 
  • #5
33,279
4,986
Sorry mistyped the function ##\frac{x}{\root{x+1}-1}##
\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}##
 
  • #6
142
1
\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}##
Hmm Sorry little mistake
 

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