1. **Problem Statement:** Determine all intervals on which the graph of the function $f$ is increasing. 2. **Understanding Increasing Intervals:** A function is increasing on intervals where its graph moves upward as $x$ increases. Formally, $f$ is increasing on an interval if for any $x_1 < x_2$ in that interval, $f(x_1) < f(x_2)$. 3. **Analyzing the Graph Description:** - The graph starts high at $y=7$ when $x=-9$ and decreases to $y=1$ near $x=-5$ (decreasing). - It continues downward to a local minimum near $y=-5$ at $x=0$ (still decreasing). - Then it rises to a local maximum near $y=3$ at $x=3$ (increasing). - Finally, it descends again towards $y=-5$ near $x=9$ (decreasing). 4. **Identifying Increasing Intervals:** - From $x=-9$ to $x=0$, the function is decreasing. - From $x=0$ (local minimum) to $x=3$ (local maximum), the function is increasing. - From $x=3$ to $x=9$, the function is decreasing again. 5. **Conclusion:** The function $f$ is increasing on the interval $$\boxed{(0,3)}.$$