Defined at a Point

Definition

When we say that a function is defined at a point, it means that there is an actual value assigned to that specific input within the domain.

Analogy

Consider attending an event with assigned seating. If someone tells you that your seat is defined at row 5, seat 10, it means there is an exact spot reserved just for you.

Related terms

Discontinuity: A property describing points where either the function is not defined or there are abrupt changes in the graph.

Vertical Asymptote: A vertical line that a graph approaches but never crosses, indicating a point where the function is undefined.

Removable Discontinuity: A type of discontinuity where a hole exists in the graph of a function, but it can be filled by redefining the value at that point.