https://file.aiquickdraw.com/mathbot/file/1727088808657pwflrmzy.jpg

Let's analyze the graph and identify the open intervals where the function is increasing and decreasing.

### Increasing Intervals:
The function is increasing where the slope of the graph is positive (i.e., where the curve is going upwards as we move from left to right).

- From approximately \(x = -\infty\) to \(x = -7\).
- From approximately \(x = -2\) to \(x = 4\).
- From approximately \(x = 7\) to \(x = \infty\).

Thus, the increasing intervals are approximately:  
\[
(-\infty, -7) \cup (-2, 4) \cup (7, \infty)
\]

### Decreasing Intervals:
The function is decreasing where the slope of the graph is negative (i.e., where the curve is going downwards as we move from left to right).

- From approximately \(x = -7\) to \(x = -2\).
- From approximately \(x = 4\) to \(x = 7\).

Thus, the decreasing intervals are approximately:  
\[
(-7, -2) \cup (4, 7)
\]

### Final Answer:
- Increasing: \((- \infty, -7) \cup (-2, 4) \cup (7, \infty)\)
- Decreasing: \((-7, -2) \cup (4, 7)\)

If you have any questions or need further clarification, feel free to ask!

Here are five related questions to expand on this:
1. How do you find the critical points of a function from its graph?
2. How do increasing and decreasing intervals relate to the derivative of a function?
3. Can a function be increasing or decreasing at a single point?
4. How do concavity and inflection points relate to the behavior of a graph?
5. What are the differences between local and absolute extrema?

**Tip:** To find increasing and decreasing intervals, check the slopes of the graph: positive slopes mean increasing, while negative slopes mean decreasing!

Identify the open intervals on which the graph of the function is increasing or decreasing. Assume that the graph extends past what is shown. Use the letter U for union. To enter ∞, type infinity.

Learn how to identify the open intervals where the graph of a function is increasing or decreasing by analyzing its curve. This example focuses on using graphical behavior and critical points to determine the function's trends. Suitable for high school students studying calculus or pre-calculus.

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