https://file.aiquickdraw.com/mathbot/file/1727100404603vpxewszk.jpg

Looking at the graph provided, the function is a smooth curve that resembles a polynomial of degree 3. We can determine the intervals where the function is increasing and decreasing by analyzing the slopes of the graph.

### Steps to identify:
- The function is **increasing** where the slope of the curve is positive (moving upwards).
- The function is **decreasing** where the slope of the curve is negative (moving downwards).

From the graph:
1. The function starts by decreasing from \( x = -\infty \) until it reaches its first local minimum at approximately \( x = -7 \).
2. It then increases from \( x = -7 \) to its local maximum at \( x = -1 \).
3. From \( x = -1 \), it decreases until it reaches a local minimum at \( x = 5 \).
4. After \( x = 5 \), the function begins to increase again as it heads towards \( x = \infty \).

### Answer:
- **Increasing intervals**: The function is increasing on the intervals \( (-7, -1) \cup (5, \infty) \).
- **Decreasing intervals**: The function is decreasing on the intervals \( (-\infty, -7) \cup (-1, 5) \).

Would you like further clarification or details on this solution?

Here are 5 related questions to expand understanding:
1. How do we identify local maxima and minima using a graph?
2. What is the difference between local and global extrema?
3. Can the derivative of a function help determine intervals of increase and decrease?
4. What are the key characteristics of a cubic function based on its graph?
5. How can you estimate inflection points from a graph?

**Tip:** To find intervals of increasing and decreasing more precisely, you can use the derivative of the function and set it equal to zero to find critical points!

Identify the open intervals on which the graph of the function is increasing or decreasing. Assume that the graph extends past what is shown.

Identify the intervals where the polynomial function is increasing or decreasing using graph analysis. This problem involves the first derivative test, critical points, and polynomial function behavior. Suitable for Grades 11-12.

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