Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.1 - Graphs and Models - Exercises - Page 8: 35

Answer

y=$\frac{x}{x^{2}+1}$

Work Step by Step

Substitute -x for x. If equation is equivalent, graph is symmetric to y-axis. y=$\frac{(-x)}{(-x)^{2}+1}$ y=$\frac{-x}{x^{2}+1}$ Equations are not equivalent, so not symmetric to y-axis. Substitute -y for y. If equation is equivalent, graph is symmetric to x-axis. (-y)=$\frac{x}{x^{2}+1}$ y=$\frac{-x}{x^{2}+1}$ Equations are not equivalent, so not symmetric to x-axis. Substitute -y for y and -x for x. If equation is equivalent, graph is symmetric to origin. (-y)=$\frac{(-x)}{(-x)^{2}+1}$ y=$\frac{x}{x^{2}+1}$ Equations are equivalent, so function symmetric about origin.
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