The question asks, "On which interval is the function increasing and non-linear?" Let's break it down using the graph.

Step-by-Step Analysis:

1. Non-Linear Behavior: Non-linear sections are where the curve bends, meaning the slope is not constant.
2. Increasing Interval: A function is increasing when the y-values go up as you move from left to right on the graph.

Looking at the Graph:

• From $-9$ to about $-6$, the function is increasing and it follows a non-linear (curved) path.
• After $x = -6$, the function decreases, then increases again between $x = 0$ and $x = 3$, but this section is not non-linear.

Conclusion:

The function is increasing and non-linear on the interval $(-9, -6)$. Therefore, the correct answer is: $\boxed{-9 < x < -6}$

Would you like further clarification or additional details? Here are some related questions:

1. What defines a non-linear function?
2. How can you identify increasing and decreasing intervals on a graph?
3. What would the slope look like in linear vs. non-linear parts of the graph?
4. Why is the interval $-9 < x < -6$ the only answer?
5. How would you calculate the exact points of increase and decrease algebraically?

Tip: Always observe the graph's curvature to determine non-linearity and look at the direction of the curve to find increasing or decreasing intervals.