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Determine whether f is continuous on each of the following intervals:
First, we'll draw the function:
Now it's easier to see what's going on.
[10,12]: f is not continuous on this interval because f(12) is undefined.
[10,12): f is continuous on this interval. For starters, f is continuous on (10, 12). While it's true that if we look at the whole graph, f is discontinuous at x = 10, but for the sake of continuity on [10,12), we only care about the right-sided limit. Since , f is continuous on [10,12).
(10,12]: f is not continuous on this interval because f(12) is undefined.