1. Given the graph of the parabola $y = f(x)$, we want to solve the inequalities $f(x) \leq 0$ and $f(x) > 0$. 2. From the graph, observe that the parabola opens upwards with vertex near $(-1.5, -4)$. 3. The parabola crosses the x-axis at approximately $x = -3$ and $x = 3$. These are the roots where $f(x) = 0$. 4. For $f(x) \leq 0$: Since the parabola opens upward, the values of $f(x)$ are less than or equal to zero between the roots. This includes the roots where $f(x)=0$. 5. Therefore, the solution for $f(x) \leq 0$ is $[-3, 3]$. 6. For $f(x) > 0$: This corresponds to the parts of the graph where $f(x)$ is above the x-axis, i.e., outside the roots. 7. Hence, the solution for $f(x) > 0$ is $(-\infty, -3) \cup (3, \infty)$. Final answers: - $f(x) \leq 0$ solution set is $[-3, 3]$. - $f(x) > 0$ solution set is $(-\infty, -3) \cup (3, \infty)$.