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

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Presentation on theme: "A function, f, is continuous at a number, a, if 1) f(a) is defined 2) exists 3)"— Presentation transcript:

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

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

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

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

6  Removable Discontinuities  Infinite Discontinuities  Jump Discontinuities

7 Function redefined at a point

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

11 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

12 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


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