From the image provided, we need to determine the intervals on which the function $f(x)$ is increasing and decreasing based on its graph.

Steps:

1. Segment 1 (from $x = -6$ to $x = -2$):

   • The graph shows that the function is rising as $x$ moves from $-6$ to $-2$. Thus, the function is increasing on this interval.

2. Segment 2 (from $x = -2$ to $x = 2$):

   • Here, the function is falling as $x$ moves from $-2$ to $2$. Hence, the function is decreasing on this interval.

3. Segment 3 (from $x = 2$ to $x = 5$):

   • The graph shows the function increasing again between $x = 2$ and $x = 5$. Therefore, the function is increasing on this interval.

Answer:

• The function is increasing on the intervals $-6 < x < -2$ (Segment 1) and $2 < x < 5$ (Segment 3).
• The function is decreasing on the interval $-2 < x < 2$ (Segment 2).

Do you need further clarification or details on this? Here are some related questions you might find useful:

1. What does it mean for a function to be increasing or decreasing graphically?
2. How do we determine where a function is increasing or decreasing using its derivative?
3. How would the behavior change if the segments had different slopes?
4. How do horizontal segments (if any) affect the increasing/decreasing nature of a function?
5. Can a function be increasing or decreasing at specific points rather than intervals?

Tip: When reading graphs, always observe the direction of the graph from left to right to determine increasing or decreasing behavior.