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Continuity of Functions

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:

  1.  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.
  2.  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. 
  3. 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).

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