Let me extract the information from the graph and the prompts in your image to solve the questions. One moment please!### Analysis of the Graph and Questions:

1. Relative Maximum

• The relative maximum occurs where the graph peaks locally. From the graph, the highest local peak appears at $x = 3$, and the function value there is approximately $y = 4$.
• Answer:
  • Relative maximum = 4 at $x = 3$.

2. Relative Minimum

• The relative minimum occurs where the graph dips locally. From the graph, the lowest local dip is at $x = -2$, and the function value there is approximately $y = -6$.
• Answer:
  • Relative minimum = -6 at $x = -2$.

3. Intervals of Increase

• The function is increasing wherever the slope of the graph is positive (going uphill).
  • Increasing interval: $(-2, 3)$ (from the minimum at $x = -2$ to the maximum at $x = 3$).
• Answer:
  • Increasing on $(-2, 3)$.

4. Intervals of Decrease

• The function is decreasing wherever the slope of the graph is negative (going downhill).
  • Decreasing intervals:
    • $(-\infty, -2)$ (from left to the minimum at $x = -2$),
    • $(3, \infty)$ (from the maximum at $x = 3$ to the right).
• Answer:
  • Decreasing on $(-\infty, -2)$ and $(3, \infty)$.

5. Domain

• The graph extends infinitely in both the left and right directions (all $x$-values are included).
• Answer:
  • Domain is $(-\infty, \infty)$.

6. Range

• The graph spans vertically from its lowest point ($y = -6$) to its highest point ($y = 4$), covering all values in between.
• Answer:
  • Range is $[-6, 4]$.

Final Answers:

1. The function has a relative maximum of 4 at $x = 3$.
2. The function has a relative minimum of -6 at $x = -2$.
3. The function is increasing on the interval $(-2, 3)$.
4. The function is decreasing on the intervals $(-\infty, -2)$ and $(3, \infty)$.
5. The domain of the function is $(-\infty, \infty)$.
6. The range of the function is $[-6, 4]$.

Do you want a detailed breakdown of any of the steps?
Here are five questions to expand on this:

1. How do you determine intervals of increase and decrease from a graph?
2. What does "domain" mean in the context of functions?
3. How do relative maxima and minima relate to the derivative of a function?
4. Can there be more than one relative maximum or minimum in a function?
5. What is the significance of the range for real-world applications?

Tip: Always analyze a graph systematically, starting with extrema, intervals, and the overall behavior of the function!