1. **State the problem:** We have the function $f(x) = x^3$ and want to analyze the effect of reflecting its graph across the x-axis and then the y-axis. 2. **Reflection across the x-axis:** Reflecting a graph across the x-axis changes $y$ to $-y$. For $f(x)$, this means the new function is $-f(x) = -x^3$. 3. **Reflection across the y-axis:** Reflecting across the y-axis changes $x$ to $-x$. Applying this to $-f(x)$ gives $-f(-x) = -(-x)^3 = -(-x^3) = x^3$. 4. **Result of both reflections:** Reflecting $f(x)$ first across the x-axis and then the y-axis returns us to the original function $f(x) = x^3$. 5. **Determine if $f$ is even, odd, or neither:** - A function is even if $f(-x) = f(x)$. - A function is odd if $f(-x) = -f(x)$. 6. For $f(x) = x^3$, check $f(-x) = (-x)^3 = -x^3 = -f(x)$, so $f$ is an odd function. **Final answers:** - Reflecting $f(x)$ across the x-axis and then the y-axis returns the original function. - The function $f(x) = x^3$ is odd.