There are two different methods of determining the continuity, or otherwise of a function. They are (i) Graphic method, and (ii) Analytical method detailed as under:
(i) Graphic Method
Under this method, the data relating to a function at a point, or points are plotted on a graph paper. If, the curve so drawn shows n breaks/gaps/jumps, throughout the interval, the function is said to be continuous. If, there appears any break, or gap in the curve, the function is said to be a discontinuous one.
(ii) Analytical Method
Under this method, the continuity, or otherwise of a function is judged by an analysis of the essential characteristics of a continuous function. If, all the characteristics cited above are satisfied, the function is said to be a continuous one, otherwise it is considered as a discontinuous function.