Find intervals on which each function is continuous...again sorry :( i'll learn, i swear xD

Question

anonymous · Answer

$$f(x)=\frac{ x ^{2} }{ 2x+4 }$$

anonymous · Answer

my answer was all real #?

anonymous · Answer

graph it and look for places where there is a large jump in y between points or where points are missing

anonymous · Answer

I would look at where the denominator is zero and see if that point exists. if it doesn't, the function cannot be continuous there.

anonymous · Answer

ok so -2 would make the denominator be 0.

anonymous · Answer

does that mean there is a hole there?

anonymous · Answer

Terenz help!!! please

terenzreignz · Answer

Rational functions like this one are continuous everywhere in their domain, so your best bet is finding a point that is not in its domain.

anonymous · Answer

Sorry, i don't really get it. i'm trying to graph it, what kind of graph is it?

terenzreignz · Answer

There is no need to graph.  Just look for the points (or x-values) for which this function has no existent value.  Points of discontinuity of rational functions are points for which the denominator becomes zero.

anonymous · Answer

So it's -2?

terenzreignz · Answer

Yes.  That seems to be the only point.

terenzreignz · Answer

But you are not asked for points of discontinuity, rather, you are asked for intervals for which this function is continuous... got that handled?

anonymous · Answer

and the intervals would be..(-infinity,2)(2,infinity)

terenzreignz · Answer

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terenzreignz · Answer

attachment

anonymous · Answer

-infinty<-2>infinity?

terenzreignz · Answer

$$\Large (-\infty,-2)\cup(-2,\infty)$$

anonymous · Answer

oh..sorry yea

anonymous · Answer

Thank you

terenzreignz · Answer

No problem.