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, \(\lim\limits_{x \rightarrow a} f(x) ≠ f(a)\).