Based on the graph provided, we can determine the intervals where the function is increasing or decreasing, and also locate the relative maxima and minima.

1. Increasing Intervals: The function is increasing when the slope of the graph is positive (rising). From the graph, the function appears to be increasing on two intervals:

   • From $x = -5$ to approximately $x = -3$
   • From $x = -2$ to $x = 0$

2. Decreasing Intervals: The function is decreasing when the slope of the graph is negative (falling). It appears to be decreasing on the following intervals:

   • From $x = -3$ to $x = -2$
   • From $x = 0$ onward (to the right of $x = 0$, the graph is falling steeply)

3. Relative Maximum: The relative maximum occurs at the highest point on a particular section of the graph. This can be seen at approximately:

   • $x = 0$, where the function reaches its peak value near $y = 4$.

4. Relative Minimum: The relative minimum occurs at the lowest point of a section of the graph. From the graph, there is a minimum around:

   • $x = -3$, where the function dips to around $y = -1$.

Summary:

• Increasing: $(-5, -3) \cup (-2, 0)$
• Decreasing: $(-3, -2) \cup (0, \infty)$
• Relative Maximum: $x = 0$ at $y = 4$
• Relative Minimum: $x = -3$ at $y = -1$

Let me know if you need further clarification or additional details!

Related Questions:

1. How do you find relative extrema algebraically?
2. Can you determine concavity and points of inflection from this graph?
3. How do increasing and decreasing intervals relate to the derivative?
4. What is the significance of relative maxima and minima in real-world problems?
5. Can this graph represent a real-life scenario?

Tip:

To confirm the intervals of increase or decrease, the first derivative of the function can be analyzed. Where it is positive, the function is increasing; where negative, it is decreasing.