https://file.aiquickdraw.com/mathbot/file/1728673083326y7u2yrjf.jpg

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! 

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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.

Consider the function in the graph to the right. The function has a maximum of ___ at x = ___, a minimum of ___ at x = ___. The function is increasing on the interval(s): ___. The function is decreasing on the interval(s): ___. The domain of the function is: ___. The range of the function is: ___.

Learn how to analyze a function from its graph by identifying maximum and minimum points, increasing and decreasing intervals, and determining the domain and range. Suitable for high school students in Grades 9-12.

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