Let's analyze the graph and fill out the provided information step-by-step.

1. Maximum and Minimum

• From the graph, you can observe that there is a local maximum point at $x = -5$, where the function reaches the highest value of 9.
• There is also a local minimum at $x = -2$, where the function reaches a value of 0.

This part of the problem already seems filled correctly in your image.

2. Increasing and Decreasing Intervals

• Increasing Intervals: A function is increasing where its slope is positive (going upwards). The graph shows the function increases:
  • From $x = -\infty$ to $x = -5$ (on the left-hand side of the maximum)
  • And again from $x = -2$ onward (after the minimum).
• Decreasing Intervals: A function is decreasing where its slope is negative (going downwards). The function is decreasing between $x = -5$ and $x = -2$ (between the maximum and minimum points).

3. Domain of the Function

• The domain of the function includes all the values of $x$ for which the function is defined. The graph appears to extend infinitely in both directions, so the domain is $(-\infty, \infty)$.

4. Range of the Function

• The range is the set of all possible $y$-values the function can take. From the graph, the function reaches a minimum value of $y = 0$ (at $x = -2$) and goes up infinitely. Therefore, the range is $[0, \infty)$.

Final Answers:

• Maximum: $9$ at $x = -5$
• Minimum: $0$ at $x = -2$
• Increasing Intervals: $(-\infty, -5) \cup (-2, \infty)$
• Decreasing Intervals: $(-5, -2)$
• Domain: $(-\infty, \infty)$
• Range: $[0, \infty)$

Let me know if you need further clarification or details!

Here are 5 related questions for further practice:

1. How can you determine if a function has a local maximum or minimum using the first derivative?
2. What does it mean for a function to be concave up or concave down, and how can this be determined from the graph?
3. Can a function have more than one absolute maximum or minimum? Why or why not?
4. What are the implications of a vertical asymptote for the domain and range of a function?
5. How do you identify inflection points on the graph of a function?

Tip: When analyzing increasing and decreasing intervals, pay attention to the slopes of the tangent lines or observe the direction of the curve visually.