https://file.aiquickdraw.com/mathbot/file/17261933608857zz1mfvx.jpg

Let's analyze the graph to determine the **domain** and **range**.

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

- Looking at the graph, the curve starts at \(x = -10\) and goes up to \(x = 10\).
- At \(x = -10\), there is a filled circle, meaning the function is defined at that point.
- At \(x = 10\), there is an open circle, indicating that the function is not defined at \(x = 10\).

Thus, the **domain** of the function is:
\[
\boxed{[-10, 10)}
\]

### Range
The **range** of a function represents all the possible values of \(y\) that the function can take.

- The graph shows that the lowest point is at \(y = -10\) and the highest point is \(y = 5\).
- The function takes values from \(y = -10\) to \(y = 5\), but at \(y = 5\), there is an open circle, meaning the function does not include \(y = 5\).

Thus, the **range** of the function is:
\[
\boxed{[-10, 5)}
\]

Would you like further details or have any questions about this? 

Here are 5 related questions to expand your understanding:
1. How does the graph of a piecewise function differ from a continuous one?
2. How do open and closed circles on a graph impact the domain and range?
3. How can you find the intervals of increase and decrease from the graph?
4. How does the vertex of the curve relate to the function's minimum or maximum value?
5. How would the domain change if the open circle at \(x = 10\) were closed?

**Tip:** Always pay attention to open and closed circles on a graph as they indicate whether the endpoints are included in the domain and range!

Analyze the domain and range of a piecewise function with open and closed intervals using a detailed graph representation. This problem covers essential concepts in graph analysis, including how open and closed circles impact domain and range. Suitable for students in Grades 9-12.

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