# Why Graphing Tools doesn't represent hole in a graph

• 22990atinesh
In summary: I used #\frac{x}{\sqrt{x+1}-1}# instead of ##\frac{x}{\sqrt{x-1}-1}##.In summary, online graphing tools do not always show discontinuities in a graph of a function.
22990atinesh
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

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

What I'm saying is that, apart from circle there must be some sort of marks representing that the function is not defined here.

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:

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

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:
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.

22990atinesh said:
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

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

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}##

22990atinesh said:
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}##

Mark44 said:
\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

## 1. Why are holes not represented in graphs?

Graphing tools are designed to plot data points and connect them with a line or curve to show a continuous relationship between the points. Holes, also known as discontinuities, do not fit into this continuous pattern and therefore cannot be properly represented on a graph.

## 2. Can't graphing tools be modified to show holes?

While it is possible to add a hole to a graph manually, it would involve breaking the continuity of the graph and would make it difficult to interpret the data accurately. Graphing tools are designed to show a clear and continuous relationship between data points, and modifying them to show holes would go against this purpose.

## 3. Are there any alternatives to graphing tools for representing holes?

Yes, there are other mathematical representations that can be used to show holes, such as piecewise functions or parametric equations. These may be more complex and less visually appealing than a traditional graph, but they can accurately depict the presence of a hole in a function.

## 4. How does not representing holes affect the accuracy of a graph?

Not representing holes in a graph can lead to a misinterpretation of the data. Holes indicate a discontinuity in a function, which can have different implications depending on the context. By not showing a hole on a graph, important information about the behavior of the function at that point is lost.

## 5. Is there any advantage to not representing holes in graphs?

One advantage of not representing holes in graphs is that it simplifies the visual representation of the data. By connecting all the data points with a continuous line or curve, the graph is easier to read and understand. Additionally, holes can be confusing for those who are not familiar with mathematical concepts, so not showing them can make graphs more accessible to a wider audience.

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