https://file.aiquickdraw.com/mathbot/file/17260953256376fd244vf.jpg

To determine the intervals over which the function \( f(x) \) is increasing, decreasing, or constant, we need to analyze the graph provided.

### Analyzing the Graph:

1. **Increasing Intervals**: A function is increasing where the graph moves upwards as we move from left to right.
2. **Decreasing Intervals**: A function is decreasing where the graph moves downwards as we move from left to right.
3. **Constant Intervals**: A function is constant where the graph remains flat or horizontal.

### Observing the Graph:

- **Increasing**: The graph increases from \( x = -3 \) to \( x = -1 \).
- **Constant**: The graph is constant (flat) from \( x = -1 \) to \( x = 2 \).
- **Decreasing**: The graph decreases from \( x = 2 \) to \( x = 4 \).

### Interval Notation:

(a) **Increasing Interval**: 
- The function is increasing on the interval:  
  \[
  (-3, -1)
  \]

(b) **Decreasing Interval**:
- The function is decreasing on the interval:  
  \[
  (2, 4)
  \]

(c) **Constant Interval**:
- The function is constant on the interval:  
  \[
  (-1, 2)
  \]

Would you like further details, or do you have any questions?

Here are some additional questions related to the graph:

1. What happens to the function's value as \( x \to -3 \)?
2. Can a function be both increasing and decreasing on the same interval?
3. How would the intervals change if there was a point of discontinuity?
4. What is the domain of the function depicted in the graph?
5. How does the graph reflect the range of the function?

**Tip**: When interpreting graphs, pay attention to the direction of movement to determine if a function is increasing, decreasing, or constant over certain intervals.

Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant.

Learn how to determine the intervals over which a function is increasing, decreasing, and constant using graph analysis. This problem uses interval notation and is suitable for students in Grades 9-12.

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