1. **Stating the problem:** We are given a graph with points at (-9,7), (-3,-2), (0,5), (4,9), and (9,0) and asked to analyze the behavior of the function $y=f(x)$ over the intervals $-9 < x < -3$, $-3 < x < 0$, $0 < x < 4$, and $4 < x < 9$. 2. **Understanding the problem:** The graph shows a continuous curve passing through these points. We want to describe the function's behavior (increasing or decreasing) on each interval. 3. **Analyzing each interval:** - On $-9 < x < -3$, the function moves from $y=7$ at $x=-9$ down to $y=-2$ at $x=-3$. This means the function is **decreasing** on this interval. - On $-3 < x < 0$, the function moves from $y=-2$ at $x=-3$ up to $y=5$ at $x=0$. This means the function is **increasing** on this interval. - On $0 < x < 4$, the function moves from $y=5$ at $x=0$ up to $y=9$ at $x=4$. This means the function is **increasing** on this interval. - On $4 < x < 9$, the function moves from $y=9$ at $x=4$ down to $y=0$ at $x=9$. This means the function is **decreasing** on this interval. 4. **Summary:** - $-9 < x < -3$: $f(x)$ is decreasing. - $-3 < x < 0$: $f(x)$ is increasing. - $0 < x < 4$: $f(x)$ is increasing. - $4 < x < 9$: $f(x)$ is decreasing. This analysis helps understand the function's behavior based on the graph's shape and points.