How Do You Apply the Intermediate Value Theorem to Various Intervals on a Graph?

[null(0)]

I have a question about applying the intermediate value theorem to graphs.

Attached is an example graph.
So, to what interval(s) could I apply the IVT? Would it be open or closed?

Also, what would be the applicable interval for a graph that has multiple zeros and is continuous; would you include all of the zeros shown on the graph in the interval?




Thanks in advance,


null(0);

 

[CompuChip]

The requirement on the intervals [a, b] is that f is continuous on them.
So for any a < b < 0 and 0 < a < b (assuming that the graph is just cut-off but it does not terminate on the left or right), [a, b] is a valid interval.
Since the graph does not clearly indicate what happens at x = 0, it is not possible to say something about it. For example, if f(0) is not defined, then this is all you can say. If f(0) = -1, then you can expand the possible intervals to a < b < 0 or 0 <= a < b.