The graph in the image appears to be a function with peaks and valleys, indicating where it increases and decreases. Let me break down how to answer the question:

Identifying Increasing and Decreasing Intervals:

1. Increasing Intervals: A function is increasing on an interval where the graph moves upwards as you move from left to right. From the graph, it appears to be increasing between:

   • From $x = -4$ to $x = -1$
   • From $x = 1$ to $x = 3$

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

   • From $x = -\infty$ to $x = -4$
   • From $x = -1$ to $x = 1$
   • From $x = 3$ to $x = \infty$

Final Answer:

• Increasing on the intervals: $(-4, -1) \cup (1, 3)$
• Decreasing on the intervals: $(-\infty, -4) \cup (-1, 1) \cup (3, \infty)$

Let me know if you need further details or clarifications!

Here are five related questions to consider:

1. What is the behavior of the function at its critical points?
2. How do you identify local maxima and minima in a graph?
3. Can a function be constant on an interval? How would that look on a graph?
4. How do the first and second derivatives help in determining increasing and decreasing intervals?
5. How can inflection points affect the increasing/decreasing nature of a function?

Tip: When analyzing graphs, always observe where the slope changes from positive to negative (or vice versa) to determine increasing and decreasing intervals.