Jump Discontinuity A jump discontinuity occurs when the right-hand and left-hand limits exist but are not equal. We’ve already seen one example of a function with a jump discontinuity: y x Figure 1: Graph of the discontinuous function listed below � f (x) = x+1 −x x>0 x≥0 This discontinuous function is seen in Fig. 1. For x > 0, lim f (x) = 1 x→ 0 but f (0) = 0. (One can also say, f is continuous from the left at 0, but not the right.) Here is another example in which lim exists, and lim also exists, but x→x+ 0 they are NOT equal. x→x− 0 x0 Figure 2: Another example of a jump discontinuity

Jump Discontinuity

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