# Continuity of Functions

# Continuity on an Interval via Pictures

Remember, *f* is continuous on an interval if we can finger paint over *f* on that interval without lifting our drawing digit.

### Sample Problem

Look at the function *f* drawn below:

- The function
*f*is continuous on the interval (-5,5) because if*c*is any point in (-5,5), . We can start our pencil out on the graph at*x*= -5 and trace the graph to x = 5 without lifting the pencil. - This function is not continuous on the interval (5,8) because
*f*is not continuous at*x*= 7. When*x*= 7 we need to lift the pencil to trace the graph. - Here's a tricky one: the function
*f*is continuous on the interval (5,7). The only point on the whole graph at which*f*is discontinuous is*x*= 7, and 7 isn't in the interval (5,7).