https://file.aiquickdraw.com/mathbot/file/1726969050041snstun8z.jpg

Let's analyze the graph and extract the relevant information:

1. **Y-intercept**: This is where the graph crosses the y-axis. Based on the graph, the y-intercept occurs at \( y = 5 \).

2. **X-intercepts**: These are the points where the graph crosses the x-axis. From the graph, the x-intercepts are at \( x = -2 \) and \( x = 6 \).

3. **Domain**: The domain is the set of all possible x-values that the function can take. The graph extends from \( x = -2 \) to \( x = 6 \). Thus, the domain is \( [-2, 6] \).

4. **Range**: The range is the set of all possible y-values that the function can take. The lowest point on the graph is \( y = 1 \), and the graph extends upward to \( y = 10 \). Thus, the range is \( [1, 10] \).

5. **Function Values**:
   - \( f(-1) \): At \( x = -1 \), the corresponding \( y \)-value is 4. Therefore, \( f(-1) = 4 \).
   - \( f(4) \): At \( x = 4 \), the corresponding \( y \)-value is 9. Therefore, \( f(4) = 9 \).

### Final Answers:
- **Y-intercept**: \( y = 5 \)
- **X-intercepts**: \( x = -2, 6 \)
- **Domain**: \( [-2, 6] \)
- **Range**: \( [1, 10] \)
- **\( f(-1) \)**: 4
- **\( f(4) \)**: 9

Would you like a further breakdown of any of these answers or additional details?

Here are 5 relative questions to deepen your understanding:
1. What are the characteristics of functions with multiple x-intercepts?
2. How would you determine the slope of the line segments in this piecewise function?
3. Can a function have more than one y-intercept? Why or why not?
4. How does the range of a function differ from its domain?
5. What are the implications of a graph having no x-intercepts?

**Tip**: The domain of a function refers to all the x-values where the function is defined, while the range covers all the possible y-values that result from plugging the x-values into the function.

Use the given graph to determine the function's domain, range, x-intercepts, y-intercept, and function values. Use interval notation for interval solutions.

Analyze the graph to determine the function's domain, range, x-intercepts, y-intercept, and function values. This exercise involves understanding how to read graph-based functions, applying concepts like intercepts and evaluating specific points. Suitable for students in Grades 9-12.

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