## Calculus 10th Edition

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