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Find the discontinuity at $f(2)$ of the function $f(x)=\dfrac{x^2-3x+2}{{x^2}+x-6}$.

I am confused. I do not understand that is there discontinuity at $2$ but it has discontinuity at $x=-2$. can you explain it please? For my point of view, there is no discontinuity at $2$ because after factorization I get $f(2)= $1/5 and before factorization I get $f(2)=0$ as well...

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    A rational function is continuous on its domain. What is the domain of $f$? – 2017-01-07
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    How did you got $f(2)=0$ ? – 2017-01-07
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    just plug x=2 into the main function – 2017-01-07
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    Sorry for previous comment, it was before the edit. – 2017-01-07
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    And actually, $f(2)$ is not defined. I mean, $2 \notin D_f$. – 2017-01-07
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    Most likely, what the question wants is that you calculate what value to "give" your function to bridge the "gap" at $x=2$. – 2017-01-07
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    you are right but if you draw the function at x=2, you get y=0; but x=3 it is continuous. how you draw the function. because between f(2) and F(-1) and f(3) function changes its sign from minus to plus – 2017-01-07
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    you are right @SteamyRoot but my question is that is there discontinuity at x=2 if yes , why? if you draw the function how you show the discontinuity? – 2017-01-07
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    @robax, if you mean $y=f(x)$, you can't get $y=0$ by putting $x=2$ in main function because $2 \notin D_f$. Another thing, if you want to "fill the gap", you should assign $f(2)=\dfrac{1}{5}$. If you will do this, the function will become continuous. – 2017-01-07
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    sorry, I do not mean this. I do not like to fill up discontinuity. I like to see how you show discontinuity on the graph. – 2017-01-07
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    @robax There is no discontinuity because your function does not exist there. In every $x$ where $f(x)$ is defined, $f$ will be continuous. – 2017-01-07

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