Chapter 1 - Functions and Limits - 1.1 Four Ways to Represent a Function - 1.1 Exercises - Page 23: 73

the function f is an odd function

Calculate $f(t)$ and $f(-t)$ $f(t)=\frac{t}{t^{2}+1}$ $f(-t)=\frac{-t}{(-t)^{2}+1}=-\frac{t}{t^{2}+1}$ therefore we can see that the function f is an odd function that satisfies $f(-x)=-f(x)$ for every x in the domain.