Point of discontinuity

Definition

A point of discontinuity occurs when there is a break or jump in the graph of a function at a specific input value. The function fails to be continuous at this point.

Related terms

Removable Discontinuity:

A removable discontinuity happens when there's a hole in the graph that can be filled by redefining or modifying the function at that particular point.

Jump Discontinuity:

A jump discontinuity occurs when there's an abrupt change in values between two distinct parts of the graph, creating an actual jump from one height to another.

Asymptote:

An asymptote is a line that serves as a boundary for how close a curve can get without touching it. Discontinuities can sometimes be related to asymptotes.