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.