Determine whether f is continuous on each of the following intervals:
First, we will 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, 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.