Thread: Intervals of Continuity

1. f(x) = (x+2)/(x^2 -4)

2. f(x) = (2x+1)/(sqrt x+4)

So if I'm doing this right, then I got (-inf,2] for the first one, and [-4,inf) for the second. But, that's just looking at a graph. So now how would you find these answers (if they are correct that is) by not looking on a graph. Is there some algebraic way of doing this? My textbook isn't helping me much with this kind of question.

Also as a side question; am I doing the interval notation correctly?

Originally Posted by nautica17

1. f(x) = (x+2)/(x^2 -4)

2. f(x) = (2x+1)/(sqrt x+4)

For continuity the function must be definded.
$\displaystyle a)\;( - \infty ,2) \cup (2,\infty )\;\& \;b)\;( - 4,\infty )$

Originally Posted by Plato

For continuity the function must be definded.
$\displaystyle a)\;( - \infty ,2) \cup (2,\infty )\;\& \;b)\;( - 2,\infty )$

But see how do you know that? Is it just something that after a while you know when you see it? I know that polynomials are always continuous, but rational functions, do you just plug some numbers in? I know this is probably a silly problem, but I've always had troubles understanding things related to domains.

Please note the correction in part b.