1. The problem is to determine whether the function $f(x) = 5x^3$ is even, odd, or neither. 2. Recall definitions: - A function is even if $f(-x) = f(x)$ for all $x$. - A function is odd if $f(-x) = -f(x)$ for all $x$. 3. Calculate $f(-x)$: $$f(-x) = 5(-x)^3 = 5(-x^3) = -5x^3$$ 4. Compare $f(-x)$ with $f(x)$ and $-f(x)$: - $f(x) = 5x^3$ - $-f(x) = -5x^3$ Since $f(-x) = -5x^3 = -f(x)$, the function satisfies the condition for being odd. 5. Conclusion: The function $f(x)=5x^3$ is an odd function because $f(-x) = -f(x)$ for all $x$.