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.
If is continuous at every point in the interval , then is continuous on the open interval .
Continuity of piece-wise functions
Discuss the continuity of
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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