To determine the domain and range from the graph of the function $g(x)$:

Domain:

The domain of a function consists of all possible values of $x$ for which the function is defined. From the graph:

• The graph starts at $x = -4$ (closed circle, meaning $g(-4)$ is defined).
• It ends at $x = 5$ (closed circle at $x = 5$, indicating the value at $g(5)$ is defined).

Thus, the domain is: $[-4, 5]$

Range:

The range is the set of all possible values of $y$ that the function can take. Observing the graph:

• The lowest point on the graph occurs at $y = 0$ (closed circle), which is the minimum value.
• The highest point on the graph occurs at $y = 3$.

Thus, the range is: $[0, 3]$

Final Answer:

• Domain: $[-4, 5]$
• Range: $[0, 3]$

Would you like further details or have any other questions? Here are some related questions for further exploration:

1. How do open and closed circles on a graph affect domain and range?
2. Can a function have a domain that extends to infinity?
3. What happens to the range if the graph has asymptotes?
4. How do you handle piecewise functions when finding domain and range?
5. How does the domain of a composite function compare to the domains of its components?

Tip: Always check if the endpoints are included or excluded by looking for closed or open circles on the graph.