Property of a function that is not continuous in a given interval of its domain.
If we consider an interval [m, n] of the domain of a function f of the real variable x and a value a of this interval, we say that the function f is discontinuous in this interval if f(a) is not defined or if \(\lim\limits_{x \rightarrow a} f(x) ≠ f(a)\).
These two cases are illustrated in the examples below.
Examples
- In the graph on the left, f(a) is not defined.
- In the graph on the right, \(\lim\limits_{x \rightarrow a} f(x) ≠ f(a)\).