https://file.aiquickdraw.com/mathbot/file/1725928045939shmsa57n.jpg

The graph represents a continuous function that changes direction multiple times. To determine the intervals where the function is increasing or decreasing, we need to focus on the behavior of the curve:

### Increasing Intervals:
The function is increasing when the slope of the curve is positive, meaning the graph goes upwards as we move from left to right.

From the graph:
- It is increasing between \(x \in (-3, -1)\) and \(x \in (0, 2)\).

### Decreasing Intervals:
The function is decreasing when the slope of the curve is negative, meaning the graph goes downwards as we move from left to right.

From the graph:
- It is decreasing between \(x \in (-5, -3)\), \(x \in (-1, 0)\), and \(x \in (2, 4)\).

### Final Answer:
- **Increasing on the interval(s):** \( (-3, -1) \cup (0, 2) \)
- **Decreasing on the interval(s):** \( (-5, -3) \cup (-1, 0) \cup (2, 4) \)

Would you like more details on why these intervals were chosen or have any further questions?

Here are some related questions:
1. How do we find the critical points of a function?
2. How do you determine concavity from a graph?
3. What is the difference between local maxima and global maxima?
4. Can a function be increasing at a point where its derivative is zero?
5. How do inflection points affect the increasing and decreasing nature of a function?

**Tip:** When analyzing the graph of a function, the points where it changes from increasing to decreasing (or vice versa) are often critical points—places where the derivative is zero or undefined.

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

Learn how to identify increasing and decreasing intervals from a graphed function. This problem covers key calculus concepts such as identifying where the slope is positive or negative and using the First Derivative Test. Suitable for students in Grades 11-12.

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