Continuity: Quiz

Problem 5

Recall that this function rounds x up to the nearest integer. At what points in the domain of f is f discontinuous?

1. At all integer values.
2. 0
3. Whenever x < 0.
4. f(x) is continuous for all real numbers.

Answers, problem 5

1. At all integer values. This is because we expect to have jumps on the graph of f(x) at each integer value. For example, f(2.5) = f(2.7) = f(2.9) = 2 on the graph of f(x) but as soon as we hit f(3), we have discontinuity and the graph abrupty jumps to 3. This happens at each integer point.

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