Jump discontinuity

Definition

A jump discontinuity occurs at a point where the left-hand and right-hand limits of a function exist but are not equal. This results in a 'jump' in the graph of the function at that point.

5 Must Know Facts For Your Next Test

1. At a jump discontinuity, $\lim_{{x \to c^-}} f(x) \neq \lim_{{x \to c^+}} f(x)$.
2. The function is not continuous at a jump discontinuity.
3. Both one-sided limits must exist for there to be a jump discontinuity.
4. A jump discontinuity often appears as a vertical gap in the graph of the function.
5. Piecewise functions frequently exhibit jump discontinuities.

Review Questions

• What is required for a point to be classified as a jump discontinuity?
• How does the graph of a function behave at a jump discontinuity?
• Can both one-sided limits exist yet still result in a type of discontinuity? If so, which type?

Related terms

Continuity: A function is continuous at a point if $\lim_{{x \to c}} f(x) = f(c)$.

Limit: The value that the output of a function approaches as the input approaches some value.

Piecewise Function: A function defined by multiple sub-functions, each applying to different intervals of the domain.