Removable Discontinuities

Definition

Removable discontinuities occur when there is a hole or gap in the graph of a function, but it can be filled to create continuity. These discontinuities are typically caused by factors like canceled out common factors in rational functions.

Related terms

Asymptote:

An asymptote is a line that a graph approaches but never touches or crosses. Vertical asymptotes can sometimes be removed to create continuity.

Piecewise Functions:

Piecewise functions are defined differently on different intervals or sections of their domain. Removable discontinuities may arise when transitioning between those sections.

Limits from Both Sides: When evaluating limits near a point where a function has a removable discontinuity, it's important to consider approaching from both sides to determine if the gap can be filled and create continuity.