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.

Analogy

Think of walking along a path and suddenly encountering an uncrossable gap or hole. This gap represents the point of discontinuity where you cannot continue smoothly along the path.

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.