Examples of Continuity of Functions
Instructions
Use this dynamic activity to explore the - definition of continuity of functions at point . Select different pages to check different functions, and you can change the given information for . Use the sketch to understand the meaning of the formal definition of function continuity, including what an " challenge" signifies, and what a sufficient " response" means.
Reflection Questions
For functions being continuous at some points, try several values and find the corresponding values that fulfill the continuity definition. What are the relationship between and its corresponding ? For functions being discontinuous at some points, try using the - definition to prove the discontinuity.