A continuous function is a mathematical function that has no abrupt changes or discontinuities in its graph. This means that the function can be drawn without lifting the pen from the paper.
A function is continuous if it satisfies the three conditions of continuity: the function is defined at the point, the limit of the function exists at that point, and the limit is equal to the value of the function at that point.
No, a continuous function cannot have a hole or jump in its graph. This would violate the condition of continuity that the limit of the function must exist at the point.
Continuous functions are essential in mathematics and science because they allow us to model and analyze real-world phenomena. They are used in areas such as physics, engineering, economics, and statistics to make predictions and solve problems.
The main difference between continuous and non-continuous functions is that the graph of a continuous function is a connected line or curve, while the graph of a non-continuous function has breaks or gaps in it. Additionally, a continuous function satisfies the three conditions of continuity, while a non-continuous function does not.