## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Remember that when a function is odd, then $f(−x)=−f(x)$ and when a function is even, then $f(−x)=f(x)$. Thus, in order to find out whether the function is even, odd, or neither, we will find $f(-x)$ . $f(x)=x^{3}-4x \\ =(-x)^{3}-4(-x)\\=-(x^{3}-4x) \\=-f(x)$ This shows that the function $f(x)$ is odd.