At which values of x is the function from the graph shown continuous? State the answers from the least to the highest, if there would be more than one.

Question

This is the graph

Answer 1

Continuous for x≤-4, -4<x≤2, 2<x<4, x>4.

Comments

How do I put in the answer? it's says incomplete on my end. Thanks

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The region between -4 and 2 can be split, so perhaps this is why you were told your answer was incomplete.

Instead of -4<x≤2, put -4<x≤-1 and -1≤x≤2.

There are other ways of showing this. The point is that at x=-1 there is continuity. So you could write:

-4<x<-1 and -1≤x≤2, or -4<x≤-1 and -1<x≤2, or even -4<x<-1, x=-1 and -1<x≤2. These all mean the same thing as -4<x≤2.

The tiny circle when filled in means that point exists. When it's not filled in it means that the point doesn't exist or is undefined, so the graph is not continuous at that point. In this case when x=-1 it is filled in and is also on the curve, so there is no break at all along this section of the curve between -4 and 2. I hope this makes it clear to you.