Continuity.

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Presentation transcript:

Continuity

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

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

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

Examples: Where are each of these discontinuous? 1) 2) 3)

Three Types of Discontinuity Removable Discontinuities Infinite Discontinuities Jump Discontinuities

Removable (Point) Discontinuity Function redefined at a point

Infinite discontinuity

Jump Discontinuity

One-sided Continuity A function is continuous from the right if and continuous from the left if

Continuous on a Interval A function is continuous on its domain

Example: Where is the function continuous?

Example Where are the following continuous 1)