![]() The behavior at \( x = 3 \) is called a jump discontinuity, since the graph jumps between two values. Jump discontinuity is when the two-sided limit doesn't exist because the one-sided limits aren't equal. Point/removable discontinuity is when the two-sided limit exists, but isn't equal to the function's value. ![]() The behaviors at \(x = 2\) and \(x = 4\) exhibit a hole in the graph, sometimes called a removable discontinuity, since the graph could be made continuous by changing the value of a single point. A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function's value.
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