A continuous function is a type of mathematical function where small changes in the input result in small changes in the output. This means that if you were to draw the function on a graph, you could do so without lifting your pencil. In more technical terms, a function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point. For a function to be continuous over an interval, it must be continuous at every point within that interval. Common examples of continuous functions include polynomial functions, trigonometric functions, and exponential functions. Understanding continuous functions is essential in calculus, particularly when studying concepts like limits and derivatives.