Precalc0105to0107-page34 - (Section 1.7: Symmetry...

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(Section 1.7: Symmetry Revisited) 1.7.4 PART C: POLYNOMIAL FUNCTIONS Short Cuts for Determining whether a Polynomial Function is Even, Odd, or Neither Let fx () be a nontrivial (or “nonzero”) polynomial written in descending powers of x , though the terms could be reordered. • Delete any terms with zero coefficients. • Nonzero constant terms have degree 0, which is an even degree. •• We could rewrite the constant term 3, for example, as 3 x 0 . •• We define 0 0 to be 1 here. If every term of has even degree, then f is even . If every term of has odd degree, then f is odd . WARNING 1 : If has a nonzero constant term, then f can’t be odd. If has a term of even degree
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This document was uploaded on 12/29/2011.

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