1. **Problem Statement:** Determine all intervals where the function $f(x) \leq 0$ based on the given graph description. 2. **Understanding the problem:** The function $f(x)$ is less than or equal to zero where the graph lies on or below the x-axis (where $y=0$). 3. **Key points from the graph:** - The curve starts below zero at $x=-9$. - It rises to a peak above $y=4$ near $x=-6$. - It crosses the x-axis at $x=-1$. - It continues downward crossing $y=-1$ at $x=1$ and goes below $y=-7$ near $x=9$. 4. **Intervals where $f(x) \leq 0$:** - From the graph, $f(x) \leq 0$ approximately for $x \leq -7.5$ (since the curve is below zero before rising to the peak). - Also, for $x \geq -1$ (since the curve crosses the x-axis at $x=-1$ and remains below or equal to zero afterwards). 5. **Final answer:** $$ \boxed{(-\infty, -7.5] \cup [-1, \infty)} $$ This means the function is less than or equal to zero on these two intervals.