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.
- (10,12):
*f* is continuous on this interval.
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