# 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 .