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.
