## Precalculus (6th Edition) Blitzer

The function at the point $a$ shows a ‘jump’ and ‘hole’ in the graph, if it is defined at that point $a$, $\ \underset{x\to a}{\mathop{\lim }}\,f\left( x \right)$ exists but $\ \underset{x\to a}{\mathop{\lim }}\,f\left( x \right)\ne f\left( a \right)$.
Since $\ \underset{x\to a}{\mathop{\lim }}\,f\left( x \right)$ exists but $\ \underset{x\to a}{\mathop{\lim }}\,f\left( x \right)\ne f\left( a \right)$, so the function cannot be continuous at the point a. The graph of such functions shows a ‘jump’ and ‘hole’ at that point $a$.