Math 22 Continuity

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 Informally, a function is continuous at  means that there is no interruption in the graph of  at .

Definition of Continuity

 Let  be a real number in the interval , and let  be a function whose domain contains the interval . The function  is continuous at  when 
 these conditions are true.
 1.  is defined.
 2.  exists.
 If  is continuous at every point in the interval , then  is continuous on the open interval .

Continuity of piece-wise functions


Polynomial function is continuous on the entire real number line (ex: is continuous on )

Rational Functions is continuous at every number in its domain. (ex: is continuous on since the denominator cannot equal to zero)

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