A function, f, is continuous at a number, a, if 1) f(a) is defined 2) exists 3)

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Presentation transcript:

A function, f, is continuous at a number, a, if 1) f(a) is defined 2) exists 3)

A function is continuous if there are no breaks in the graph

At what points on the graph below is the function discontinuous?

Where are each of these discontinuous? 1) 2) 3) 4)

 Removable Discontinuities  Infinite Discontinuities  Jump Discontinuities

Function redefined at a point

A function is continuous from the right if and continuous from the left if

A function is continuous on an interval if it is continuous at every number on the interval - if f is defined on only one side of an endpoint, it is continuous from the right or left

Show that is continuous on the interval [-1,1] - need to show that it is continuous from the right to -1 and continuous from the left to 1