Question: Function f is graphed. According to the graph, is f even, odd, or neither? Choose 1 answer: A Even B Odd C Neither The graph shows a single blue function labeled f on a coordinate plane centered at the origin; the curve has a local maximum near $(-2, 6)$, crosses near $(0, 0)$, dips to a local minimum near $(2.5, -6.5)$, then rises steeply, so position_hint = center.

1. **State the problem:** Determine whether the function $f$ is even, odd, or neither based on its graph. 2. **Recall definitions:** - A function $f$ is **even** if $f(-x) = f(x)$ for all $x$ in the domain. Graphically, this means the graph is symmetric about the $y$-axis. - A function $f$ is **odd** if $f(-x) = -f(x)$ for all $x$ in the domain. Graphically, this means the graph is symmetric about the origin. 3. **Analyze the graph:** - The graph has a local maximum near $(-2, 6)$ and a local minimum near $(2.5, -6.5)$. - For an even function, the value at $-2$ should equal the value at $2$, but here $f(-2) \approx 6$ and $f(2) \approx$ not equal to $6$ (since minimum near $2.5$ is about $-6.5$). - For an odd function, $f(-2)$ should be the negative of $f(2)$, but $6$ is not the negative of approximately $-6.5$. 4. **Conclusion:** The function is neither even nor odd because it does not satisfy the symmetry conditions for either. **Final answer:** C Neither