1. The problem states that as $x$ approaches negative infinity, $f(x)$ also approaches negative infinity. We want to understand the behavior and overall shape of the function $f(x)$ based on this description and the graph. 2. From the graph description, we observe that: - At $x = -4$, $f(x) \approx -4$, which is low on the y-axis. - The graph rises to a peak slightly below $4$ around $x = -2$. - Then the graph dips to about $0$ at $x = 0$. - It rises again to a peak near $3$ at $x = 2$. - Finally, it falls steeply to about $-4$ at $x = 4$. 3. The given limit behavior as $x \to -\infty$ means the left end of the graph goes down without bound. This matches the starting point at $x = -4$ being low and the trend continuing downward. 4. The graph shows multiple turning points (i.e., points where the function changes from increasing to decreasing or vice versa), suggesting that $f(x)$ is likely a polynomial with degree at least 4 or has oscillatory features. 5. To summarize, the key points are: - $f(x) \to -\infty$ as $x \to -\infty$. - The function has at least two local maxima near $x = -2$ and $x = 2$. - The function crosses or touches the $x$-axis near $x = 0$. - The right end decreases steeply as well. This behavior fits a polynomial with a negative leading coefficient of an even degree, such as a quartic with negative leading coefficient. **Final answer:** The function $f(x)$ decreases without bound as $x \to -\infty$ and has multiple turning points with local maxima near $x = -2$ and $x = 2$, consistent with a quartic polynomial with negative leading coefficient.