Analysis of the Graph:

1. Domain: The domain represents all the possible $x$-values for which the graph is defined. From the graph:

   • The graph starts at $x = -4$ (open circle, meaning not included).
   • The graph ends at $x = 2$ (closed circle, meaning included).

   Domain in interval notation: $(-4, 2]$

2. Range: The range represents all the possible $y$-values covered by the graph. From the graph:

   • The minimum $y$-value is $-10$ (reached at $x = 2$, closed circle, so included).
   • The maximum $y$-value is $1$ (reached at $x = -2$, open circle, so not included).

   Range in interval notation: $(-10, 1)$

Would you like further clarification or assistance with another part of this problem?

Related Questions:

1. How can you verify if a graph represents a function using the vertical line test?
2. What is the significance of open and closed circles in determining the domain and range?
3. How do you determine the range when the graph has discontinuities?
4. Could the domain or range of a graph ever include infinity? Under what conditions?
5. Why is interval notation useful in describing domains and ranges?

Tip:

Always check for open and closed points when interpreting domains and ranges; they indicate whether endpoints are included or excluded.