Continuity of Functions
Continuity at a Point via Formulas
It's good to have a feel for what continuity at a point looks like in pictures. However, sometimes we are asked about the continuity of a function for which we're given a formula, instead of a picture. When this happens, remember that the following three statements must all hold for f to be continuous at c.
- I. The function f is defined at x = c.
- The limit exists.
- The value f(c) agrees with the limit .