The principle idea of a continuous function is that its graph is continuous, meaning that it can be drawn without lifting the pencil from the paper.
Continuous Function at a Point
A function f(x) is continuous at a point, x = a, if and only if it meets the following conditions:
1. The point x = a has image.
2. There is a limit of the function f(x) at x = a.
3. The value of the function at the point coincides with the limit of the function at the point.
Study the continuity of at x =2.
A function f(x) is continuous at a point if it is left-continuous and right-continuous at the point.