1. The problem is to understand why the function is odd and not even. 2. Recall the definitions: - A function $f(x)$ is even if $f(-x) = f(x)$ for all $x$ in the domain. - A function $f(x)$ is odd if $f(-x) = -f(x)$ for all $x$ in the domain. 3. To check if a function is odd, substitute $-x$ into the function and simplify. 4. If the result equals $-f(x)$, then the function is odd. 5. For example, consider $f(x) = x^3$: - Compute $f(-x) = (-x)^3 = -x^3 = -f(x)$. - Since $f(-x) = -f(x)$, $f(x)$ is odd. 6. This means the graph of an odd function is symmetric about the origin. 7. Conversely, if $f(-x) = f(x)$, the function is even and symmetric about the y-axis. 8. Therefore, if your function satisfies $f(-x) = -f(x)$, it is odd and not even. Final answer: The function is odd because it satisfies $f(-x) = -f(x)$, not $f(-x) = f(x)$.