AP Calculus AB and BC glossary
Jump discontinuity
Also called: Step discontinuity
A jump discontinuity occurs at a point where both one-sided limits exist but disagree, so the graph steps abruptly from one value to another. Because the one-sided limits differ, the two-sided limit does not exist and no redefinition can repair the break.
Jump discontinuities are the signature of piecewise functions whose pieces do not meet, and of step functions such as the greatest integer function. To find one, evaluate both one-sided limits and compare.
A common exam task is to choose a constant that makes a piecewise function continuous. Set the left-hand limit equal to the right-hand limit and solve, then confirm the shared value also equals the function value at the seam.
Appears in: Unit 1: Limits and Continuity