https://file.aiquickdraw.com/mathbot/file/1725584140876jbpgfpih.jpg

To determine the intervals where the function is increasing or decreasing, we need to observe where the graph goes upwards or downwards as we move from left to right.

### Increasing Intervals:
The function is increasing when the graph moves upwards. From the graph:
1. The function increases from approximately \((-4, 2)\) to \((-2, 0)\).
2. It also increases from approximately \((0, -2)\) to \((2, 2)\).

So, the increasing intervals are:
- \((-4, -2)\)
- \((0, 2)\)

### Decreasing Intervals:
The function is decreasing when the graph moves downwards. From the graph:
1. The function decreases from approximately \((-∞, -4)\).
2. It also decreases from approximately \((-2, 0)\) to \((0, -2)\).
3. Finally, it decreases from \((2, 2)\) to \((∞, ∞)\).

So, the decreasing intervals are:
- \((-∞, -4)\)
- \((-2, 0)\)
- \((2, ∞)\)

Would you like to see more details or have any further questions?

Here are five related questions that might help expand on this topic:

1. How can you find intervals of increase and decrease using derivatives?
2. What are the critical points of a function, and how are they related to intervals of increase and decrease?
3. How do you determine concavity and inflection points from a graph?
4. What role do maxima and minima play in determining increasing and decreasing intervals?
5. How can you use the first derivative test to determine the nature of intervals?

**Tip:** To confirm the intervals where a function is increasing or decreasing, you can use the first derivative test.

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

Learn how to identify the increasing and decreasing intervals of a function from its graph. This example focuses on interpreting the movement of a function and applying the first derivative test for accurate results. Suitable for students in Grades 10-12.

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