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Easy: One-sided limits
The left-hand limit is the height the graph approaches as x comes toward a from the left; the right-hand limit is the height it approaches from the right. The two-sided limit exists only when they are equal. An open dot is a point that is missing; a closed dot shows the function's value. f is continuous at a when the limit exists and equals f(a). When the one-sided limits differ it's a jump; when they agree but f(a) is different or missing it's a removable discontinuity (a hole).
Use the graph of y = f(x) to answer each question.
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Yes. At a hole, the graph approaches the same height from both sides, so the limit exists even though f(a) is undefined.
f(a) is defined, the limit as x → a exists, and the limit equals f(a). If any one fails, f is not continuous there.
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