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The problem asks you to describe the piecewise function using interval notation based on the graph provided. Let's analyze the graph and identify the different segments of the piecewise function:

1. **First Interval:**
   - The function is at \( f(x) = 3 \) for values of \( x \) between -4 and -2, inclusive of -4 but not -2. 
   - Interval: \([-4, -2)\)

2. **Second Interval:**
   - The function is at \( f(x) = 5 \) for values of \( x \) between -2 and 1, inclusive of -2 but not 1.
   - Interval: \([-2, 1)\)

3. **Third Interval:**
   - The function is at \( f(x) = -4 \) for values of \( x \) between 1 and 3, inclusive of 1 but not 3.
   - Interval: \([1, 3)\)

Given this information, the piecewise function description would be:

\[
f(x) = \begin{cases} 
3 & \text{if } x \in [-4, -2) \\
5 & \text{if } x \in [-2, 1) \\
-4 & \text{if } x \in [1, 3)
\end{cases}
\]

Would you like more details on how these intervals were determined? 

Here are some related questions to deepen your understanding:

1. How would you graph a piecewise function if given the intervals and function values?
2. What is the significance of open and closed circles in the graph of a piecewise function?
3. How does the concept of continuity apply to piecewise functions?
4. Can you describe the process of finding the domain of a piecewise function?
5. How would the graph look if we changed the values of \(f(x)\) for any of the intervals?

**Tip:** Always pay attention to whether the circles on the graph are open or closed, as this affects whether an endpoint is included in the interval.

Complete the description of the piecewise function graphed below. Use interval notation to indicate the intervals.

Learn how to describe a piecewise function using interval notation based on a graph. This problem involves analyzing a graph to determine the different segments of the function, suitable for students in Grades 9-12.

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