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. Continuous functions do not have any breaks, jumps, or holes in their graphs. In more formal terms, a function f(x) is continuous at a point c if three conditions are met: f(c) is defined, the limit of f(x) as x approaches c exists, and the limit equals f(c) . Continuous functions are important in calculus and are often studied in relation to concepts like limits and derivatives.