https://file.aiquickdraw.com/mathbot/file/1725503378967lpjlwn48.jpg

In order to analyze the function from the graph, I'll help determine the intervals on which it is increasing and decreasing.

### Steps:
1. **Increasing Intervals**: The function is increasing wherever the slope of the graph is positive (i.e., as you move from left to right, the graph goes up).
2. **Decreasing Intervals**: The function is decreasing wherever the slope of the graph is negative (i.e., as you move from left to right, the graph goes down).

Let me examine the image closely and describe the intervals based on the graph.

### Graph Analysis:
- The graph appears to be a cubic function or similar, showing several peaks and valleys.
- **Decreasing Intervals**: The graph starts decreasing from the far left (negative side) up to a certain point (likely near \( x = -1 \)).
- **Increasing Intervals**: After that, the graph increases up to another peak (probably near \( x = 1 \)), then decreases again.

I'll specify the intervals next:

1. **Increasing on intervals**:
   - From approximately \( x = -1 \) to \( x = 1 \).
   - The function increases between these points (from a valley to a peak).

2. **Decreasing on intervals**:
   - From \( x = -\infty \) to \( x = -1 \).
   - After the peak, the function decreases again from \( x = 1 \) to the right (i.e., \( x = \infty \)).

The increasing and decreasing intervals look like:
- **Increasing**: \( (-1, 1) \)
- **Decreasing**: \( (-\infty, -1) \cup (1, \infty) \).

Would you like more details or have any questions? Here are some related topics that might help:

1. How do you identify critical points on a graph?
2. What is the significance of a function's derivative in determining intervals?
3. Can you explain how concavity relates to increasing/decreasing intervals?
4. How do you find the maximum or minimum points in a function?
5. What role do inflection points play in analyzing graphs?

**Tip:** The first derivative of a function gives you insights into where a function is increasing or decreasing.

The function graphed above is increasing on the interval(s) and decreasing on the interval(s).

Learn how to determine the increasing and decreasing intervals of a function based on its graph. This problem explores key calculus concepts, including the first derivative test and critical points. Suitable for students in Grades 10-12.

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