To analyze the graph of the function and determine where it is increasing or decreasing, follow these steps:

1. Increasing Intervals: A function is increasing on an interval where the graph is moving upwards as you move from left to right.

2. Decreasing Intervals: A function is decreasing on an interval where the graph is moving downwards as you move from left to right.

Steps to solve the problem:

• Identify Critical Points: Look at where the function changes direction, i.e., where it has peaks (local maxima) or troughs (local minima). These points will help you determine the intervals.

Observations from the Graph:

1. The graph decreases from $x = -\infty$ to about $x = -1$.
2. It increases from $x = -1$ to $x = 1$.
3. It decreases again from $x = 1$ to about $x = 3$.
4. Finally, it increases from $x = 3$ onwards.

Therefore:

• Increasing Intervals: The function is increasing on the intervals $(-1, 1)$ and $(3, \infty)$.
• Decreasing Intervals: The function is decreasing on the intervals $(-\infty, -1)$ and $(1, 3)$.

Would you like further details or have any questions?

Here are 5 related questions:

1. What are local maxima and minima, and how do they relate to increasing and decreasing intervals?
2. How would you determine the intervals of concavity from a graph?
3. What is the importance of the first derivative in identifying increasing and decreasing intervals?
4. How can you determine whether a function is increasing or decreasing using algebraic methods?
5. How do points of inflection affect the intervals of increase and decrease in a function?

Tip: When analyzing graphs, always note the behavior of the function around critical points to determine the nature of intervals.