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.