https://file.aiquickdraw.com/mathbot/file/1727458746220x5ybh4lw.jpg

The graph presented shows a piecewise-defined function. To determine the **domain** and **range** of the function:

### Domain:
The domain represents all the possible \( x \)-values (input values) for which the function is defined. Based on the graph:
- The graph starts at \( x = -7 \) and ends at \( x = 8 \), but there is a break between \( x = -1 \) and \( x = 2 \).
- So, the domain is \( [-7, -1] \cup [2, 8] \).

Thus, the correct answer for the domain is **A. \([-7, -1] \text{ and } [2,8]\)**.

### Range:
The range represents all the possible \( y \)-values (output values) the function can take. Looking at the graph:
- The minimum \( y \)-value is \( -8 \) (at the leftmost point) and the maximum is \( 8 \) (at the top-right point).
- The graph covers all \( y \)-values between \( -8 \) and \( 8 \).

Thus, the correct answer for the range is **D. \([-8, 8]\)**.

Would you like more detailed explanations or have any questions?

Here are five related questions to expand your understanding:
1. How do you determine if a graph has breaks in its domain?
2. Can a graph have a domain that is all real numbers?
3. How would the domain change if there were vertical asymptotes?
4. What is the difference between the domain and range of a function?
5. How would you identify the range if the graph extended infinitely in the vertical direction?

**Tip:** When analyzing a graph, always check for any gaps or jumps in the \( x \)-axis for the domain and the \( y \)-axis for the range.

Find the domain and range of the piecewise-defined function whose graph is shown in the image.

Analyze the graph of a piecewise-defined function to find its domain and range. This problem helps students practice interpreting function behavior, gaps, and key concepts of domains and ranges. Suitable for Grades 9-12.

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