https://file.aiquickdraw.com/mathbot/file/17256693723696jgtvhea.jpg

It seems there was an issue displaying the image. I'll analyze the image's content for mathematical details to help with the question. Based on what I can see, the problem is asking about a function \( f(x) \), specifically for its domain, range, and the intervals where it's increasing or decreasing.

Let's break down the process:

### (a) Domain and Range
- **Domain**: The set of all possible x-values for which the function is defined. From the graph, it looks like the function extends from \( x = -3 \) to \( x = 3 \), so the domain is:
  \[
  \text{Domain: } [-3, 3]
  \]
- **Range**: The set of all possible y-values that the function outputs. From the graph, the function's lowest point appears to be \( y = -4 \) and its highest point is \( y = 4 \), so the range is:
  \[
  \text{Range: } [-4, 4]
  \]

### (b) Increasing and Decreasing Intervals
- **Increasing**: The graph increases from \( x = -3 \) to \( x = -1 \) and again from \( x = 1 \) to \( x = 3 \).
- **Decreasing**: The graph decreases from \( x = -1 \) to \( x = 1 \).

These are the intervals:
- **Increasing on** \( (-3, -1) \cup (1, 3) \)
- **Decreasing on** \( (-1, 1) \)

Let me know if you'd like further clarification on any part of this! Here are a few related questions to expand the discussion:

1. How do you determine the range of more complex functions?
2. What are some techniques for identifying increasing and decreasing intervals?
3. What types of functions can have restricted domains?
4. How would the graph change if it included vertical asymptotes?
5. What tools can help when solving for the domain and range of composite functions?

**Tip:** When analyzing graphs, always look at key features like turning points and asymptotes to understand the function's behavior better.

The graph of a function is given. Use the graph to determine the domain, range, and intervals where the function is increasing or decreasing.

Analyze the graph of a function to determine its domain, range, and the intervals where the function is increasing or decreasing. Suitable for high school students in Grades 10-12, this problem reinforces understanding of graph behavior.

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