(Section 1.7: Symmetry Revisited) 1.7.1 SECTION 1.7: SYMMETRY REVISITEDLEARNING 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 functionsand odd functions, whose graphs in the xy-plane were symmetricabout the y-axisand the origin, respectively. • We will now systematizeour study of these functions and their graphical symmetries. We will discuss useful short cutsfor identifying even functions and odd functions, and we will show how to provethem rigorously. We will also extend related symmetries to graphs of general equationsin xand y. • A zero functionf, where fx()=0 (on any domain), will be called a trivial function. If its domain is symmetric about 0, then it is botheven and odd. • Symmetry will prove helpful when graphing functions and equations
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