# Thread: Very stupid continuity question

1. ## Very stupid continuity question

Is the function (x^2 - 4)/(x + 2) continous at x=-2 ?

I am doubtful because
1. It can be reduced to (X-2) so it is continous everywhere.
2. But on the other hand isnt continuity checked for the exact function without making changes to it? Cos if x=-2 then the original function is not defined at all.

2. $\displaystyle \frac{(x^2 - 4)}{(x + 2)}$ = $\displaystyle \frac{(x+2) (x-2) }{(x + 2)}$
It is not continuous at $\displaystyle x = -2$. There is a hole there

3. Originally Posted by champrock
.....if x=-2 then the original function is not defined at all.
And that is the reason why the function is not cts at x=-2.

For continuity, the behavior at the point must agree with the behavior near the point. Approaching x=-2, you get a limit. At the point, the function is not even defined. Thus the hole, as mentioned above.