https://file.aiquickdraw.com/mathbot/file/1725948078737u1f87l4b.jpg

To find the range of the function depicted in the graph, let's analyze the y-values the graph covers:

1. **From \(x = -\infty\) to \(x = -4\)**: The function is a horizontal line at \(y = 3\) but is not defined at \(x = -4\) due to the open circle, so \(y = 3\) is included.
   
2. **At \(x = -4\)**: There is a filled point at \(y = 1\). So, \(y = 1\) is included.

3. **From \(x = -4\) to \(x = -2\)**: The function decreases linearly, covering \(y\) values from \(1\) to \(-1\). Both endpoints are included as filled points.

4. **At \(x = -2\)**: The function is defined at \(y = -1\).

5. **From \(x = -2\) to \(x = 0\)**: The function dips to a minimum at approximately \(y = -2\).

6. **At \(x = 0\)**: There is an open circle at \(y = -1\), so \(y = -1\) is not included here.

7. **For \(x > 0\)**: The function rises quickly, covering all values greater than \(y = 0\).

**Range**:
\[
\text{Range} = (-2, -1) \cup [0, \infty) \cup \{1, 3\}
\]

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Here are five related questions:

1. How would you find the domain of this graph?
2. What type of discontinuities does the graph have?
3. How do the open and closed circles affect the range?
4. How can you determine intervals of increase and decrease from the graph?
5. What is the minimum value of the function, and where does it occur?

**Tip:** When finding the range of a graph, pay close attention to open and closed circles, as they indicate whether endpoints are included or excluded.

Learn how to find the range of a function by analyzing a graph with discontinuities. This problem covers key mathematical concepts like function range, open and closed circles, and intervals. Suitable for high school students in Grades 9-12.

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