In mathematics, a function is said to be continuous if its graph can be drawn without lifting the pen. In other words, there are no breaks or jumps in the graph. There are several ways to check if a function is continuous. One way is to use the epsilon-delta definition of continuity. This definition states that a function is continuous at a point x if for every positive number epsilon, there is a positive number delta such that if |x – a| < delta, then |f(x) – f(a)| < epsilon.
Another way to check if a function is continuous is to use the limit definition of continuity. This definition states that a function is continuous at a point x if the limit of the function as x approaches a is equal to the value of the function at a. That is,