Chapter 3 - Review Exercises - Page 269: 21

Odd

To find out if the function is even, odd, or neither, we find $f(−x)$ and compare the result to $f(x)$: $f(x)=\displaystyle \frac{x}{1+x^{2}}$ $\displaystyle f(-x)=\frac{-x}{1+(-x)^{2}}$ $\displaystyle =\frac{-x}{1+x^{2}}$ $=-\displaystyle \frac{x}{1+x^{2}}$ $=-f(x)$ Thus $f(x)$ is odd.