The problem asks for the domain and range of the function based on the graph provided. Let's analyze the graph step by step.

Domain:

The domain refers to the set of all possible $x$-values that the function can take. From the graph:

• The function starts at $x = -4$ and ends at $x = 3$.
• So, the domain is all $x$-values from $-4$ to $3$.

Thus, the domain in interval notation is: $[-4, 3]$

Range:

The range refers to the set of all possible $y$-values that the function outputs. From the graph:

• The lowest point is at $y = -2$ and the highest point is at $y = 5$.
• So, the range is all $y$-values from $-2$ to $5$.

Thus, the range in interval notation is: $[-2, 5]$

Final Answer:

• Domain: $[-4, 3]$
• Range: $[-2, 5]$

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you determine the domain and range from an equation instead of a graph?
2. What is the difference between closed and open intervals in domain and range?
3. How would the domain and range change if the graph extended beyond $x = 3$?
4. How do asymptotes affect the domain and range of functions?
5. Can the domain and range ever be infinite?

Tip: Always check whether the endpoints of the domain and range are included (closed interval) or excluded (open interval) when writing in interval notation.