In Exercises 1–4, say whether the function graphed is continuous on [−1, 3]. If not, where does it fail to be continuous and why?
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A function is continuous on an interval if it is defined at every point in that interval and does not have any breaks, jumps, or holes. Specifically, for a function to be continuous at a point, the limit of the function as it approaches that point must equal the function's value at that point.

Discontinuities can be classified into three main types: removable, jump, and infinite. A removable discontinuity occurs when a function is not defined at a point but can be made continuous by defining it appropriately. A jump discontinuity happens when the left-hand and right-hand limits at a point do not match, while an infinite discontinuity occurs when the function approaches infinity at a certain point.

To determine continuity, evaluating limits is essential. The limit of a function as it approaches a point from both sides must exist and be equal to the function's value at that point. If the limits differ or do not exist, the function is discontinuous at that point, which can help identify where the function fails to be continuous.