Having defined continuity of a function at a given point, now we make a natural
extension of this definition to discuss continuity of a function Definition 2 A real function f is said to be continuous if it is continuous at every point
in the domain of f This definition requires a bit of elaboration Suppose f is a function defined on a
closed interval [a, b], then for f to be continuous, it needs to be continuous at every
point in [a, b] including the end points a and b