157LN03-functions.pdf - Symmetry Transformations and...

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Symmetry, Transformations and Compositions Math 157 Calculus I for the Social Sciences Lecture 3 based on “Calculus Early Transcendentals Differential & Multi-Variable Calculus for Social Sciences” Symmetry, Transformations and Compositions This text, including the art and illustrations, are available under the Creative Commons license (CC BY-NC-SA), allowing anyone to reuse, revise, remix and redistribute the text. For more info visit Calculus Early Transcendentals Differential & Multi-Variable Calculus for So- cial Sciences was adapted by Petra Menz and Nicola Mulberry from Lyryx’ lec- ture notes by Michael Cavers licensed under a Creative Commons Attribution Non-Commercial Share-Alike 3.0 Unported License (CC BY-NC-SA 3.0). The adaptation ensures congruency between the text Calculus Early Transcenden- tals Differential & Multi-Variable Calculus for Social Sciences and the lectures for MATH 157. 1
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Symmetry, Transformations and Compositions Math 157 Calculus I for the Social Sciences Lecture 3 Symmetry, Transformations and Compositions Learning Outcomes – Detailed: The successful student will be able to 1. Transform elementary functions. 2. Model supply, demand, cost, revenue and profit using elementary functions. 3. Perform algebra with functions. 4. Determine the equilibrium point when working with supply and demand. 5. Determine the break-even point when working with cost, revenue and profit. 2
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Symmetry, Transformations and Compositions Even and Odd Functions A function f is an even function if f ( - x ) = f ( x ), for all x in the domain of f . If you reflect the graph about the y -axis, the graph stays the same! A function f is an odd function if f ( - x ) = - f ( x ), for all x in the domain of f . If you rotate the graph 180 about the origin, the graph stays the same!
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