CalcNotes0208-page11 - (Section 2.8 Continuity 2.8.11 PART...

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(Section 2.8: Continuity) 2.8.11 PART G: CONTINUITY THEOREMS AND EXAMPLES Algebra of Continuity If f and g are functions that are continuous at a , then so are the functions f + g , f ± g , and fg . • The function f g is, also, if ga () ± 0 . • The function f n is, also, if n is a positive integer. • The function f n is, also, if: • ( n is an odd positive integer), or • ( n is an even positive integer, and fa > 0 .) In a manner similar to the limit properties in Section 2.2, Part A, the theorem above, together with the fact that constant functions and the identity function (represented by fx = x ) are everywhere continuous (on ± ), justifies the following: Continuity of Rational Functions A rational function is continuous on its domain.
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