A continuous function is a mathematical function where the graph of the function has no breaks or gaps. This means that the function is defined for all values within its domain and there are no sudden jumps or interruptions in the graph.
One example of a continuous function is the linear function, f(x) = mx + b. This function is continuous for all values of x since there are no breaks or gaps in its graph, which is a straight line.
A function is continuous if it satisfies the three conditions of continuity: the function is defined at the point, the limit of the function at that point exists, and the limit is equal to the value of the function at that point.
Yes, a function can be continuous at some points and discontinuous at others. This means that the function is defined and smooth in some areas, but may have breaks or gaps in other areas.
Continuity is important in mathematics and science because it allows us to accurately model and predict real-world phenomena. It also helps us to understand the behavior of functions and solve problems using mathematical techniques.