Types of Discontinuities - Jump Discontinuity

Definition

A jump discontinuity occurs when there is a sudden jump or gap in the graph of a function at a specific point. This means that the left-hand limit and right-hand limit exist but are not equal to each other.

Related terms

Removable Discontinuity:

A removable discontinuity occurs when there is a hole or gap in the graph of a function at a specific point, but it can be filled by redefining the function at that point.

Infinite Discontinuity:

An infinite discontinuity occurs when the left-hand limit and/or right-hand limit of a function approaches positive or negative infinity at a specific point. This results in vertical asymptotes in the graph.

Oscillating Discontinuity: An oscillating discontinuity occurs when the function oscillates infinitely between two values as x approaches a certain point. It creates an erratic behavior in the graph.