https://file.aiquickdraw.com/mathbot/file/1729191999872zuhmx94t.jpg

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.

The graph of a function is shown below. On which interval is the function increasing and non-linear?

Learn how to identify intervals where a function is increasing and non-linear by analyzing its graph. This problem helps students in Grades 9-12 understand key graph behaviors such as increasing, decreasing, and non-linearity.

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