To determine the domain and range of the given function based on the graph:

Domain:

The domain represents all possible x-values (horizontal axis) where the function is defined. Looking at the graph:

• The function starts at $x = -4$ (inclusive, as there is a filled circle) and ends at $x = 2$ (inclusive, as there is also a filled circle).

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

Range:

The range represents all possible y-values (vertical axis) of the function. From the graph:

• The y-values start at $y = -10$ (inclusive, due to the filled circle) and go up to $y = 2$ (inclusive, as the graph reaches $y = 2$).

Range in interval notation: $[-10, 2]$

Final Answer:

• Domain: $[-4, 2]$
• Range: $[-10, 2]$

Would you like a detailed explanation of why this interval was chosen, or do you have additional questions?

Related Questions:

1. How do you identify a function's domain and range from a graph?
2. What happens to the domain and range if a function has an open circle instead of a closed one?
3. Can a function have a domain or range that is not continuous?
4. How would you write the domain and range for a function with infinite intervals?
5. What are some common types of functions and their typical domains and ranges?

Tip: Always look for open and closed circles on graphs; they indicate whether the endpoints are included or excluded!