Web Reference: A function is continuous when its graph is a single unbroken curve ... that you could draw without lifting your pen from the paper. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is not continuous. Feb 23, 2026 · A function is said to be continuous on an interval if it is continuous at every point within that interval. In other words, the graph of the function shows no breaks, jumps, or discontinuities throughout the interval.
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