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To determine the **domain** and **range** of the given piecewise function from the graph, we'll analyze the points and the intervals shown in the graph.

### Domain:
The **domain** refers to all the possible values of \(x\) for which the function is defined. 

From the graph, the function spans from \(x = -6\) to \(x = 7\), and it is defined at every point within this interval (no breaks or undefined points).

Thus, the domain is:
\[
\boxed{[-6, 7]}
\]

### Range:
The **range** refers to all the possible values of \(y\) that the function can take.

From the graph, the lowest \(y\)-value is \(-3\) (at \(x = 4\)), and the highest \(y\)-value is 9 (at \(x = -2\)).

Thus, the range is:
\[
\boxed{[-3, 9]}
\]

Would you like more details on how this was derived or any further questions?

Here are 5 related questions you can explore:
1. What are the values of the function at the endpoints of the domain?
2. How would the domain and range change if the graph were shifted vertically or horizontally?
3. How can you express this function in piecewise form?
4. How does the continuity of the function affect its domain and range?
5. What happens to the domain and range if we restrict the function to a smaller interval?

**Tip:** Always use closed brackets \([a, b]\) in interval notation if the endpoints are included (solid dots on the graph).

Enter the domain and range of the piecewise function from the graph.

Learn how to determine the domain and range of a piecewise function by analyzing a graph. This problem covers fundamental graphing concepts, including interval notation, domain, and range. Suitable for students in Grades 7-9.

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