Precalc0105to0107-page31

Precalc0105to0107-page31 - (Section 1.7: Symmetry...

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(Section 1.7: Symmetry Revisited) 1.7.1 SECTION 1.7: SYMMETRY REVISITED LEARNING OBJECTIVES • Recognize short cuts for identifying even functions and odd functions. • Be able to justify those short cuts using proofs. • Use equations to identify symmetries in their graphs. PART A: DISCUSSION • In Section 1.3, we defined even functions and odd functions , whose graphs in the xy -plane were symmetric about the y -axis and the origin , respectively. • We will now systematize our study of these functions and their graphical symmetries. We will discuss useful short cuts for identifying even functions and odd functions, and we will show how to prove them rigorously. We will also extend related symmetries to graphs of general equations in x and y . • A zero function f , where fx () = 0 (on any domain), will be called a trivial function . If its domain is symmetric about 0, then it is both even and odd. • Symmetry will prove helpful when graphing functions and equations
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