Let's analyze the graph to determine the domain and range of the function $g$, then express them in interval notation.

Domain:

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

• The function starts at $x = -4$ (where the left-most point is) and ends at $x = 3$ (where the right-most point is).
• Both endpoints are closed circles, indicating the points are included in the domain.

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

Range:

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

• The highest point on the graph is $y = 3$ (at $x = -4$).
• The lowest point on the graph is $y = -4$ (at $x = 3$).
• Both endpoints are included, as represented by the closed circles.

Thus, the range is: $[-4, 3]$

Final Answer:

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

Would you like a detailed explanation of any of these steps, or do you have any other questions?

Related Questions:

1. How can you find the domain of a function algebraically instead of graphically?
2. What are the differences between open and closed intervals in domain/range?
3. Can you explain why closed circles represent inclusion of the endpoint in the domain and range?
4. How would the domain and range change if there were vertical or horizontal asymptotes?
5. Can you describe how to find the range of a more complex function like a quadratic or cubic?

Tip: Always check endpoints of the graph carefully. Open circles indicate exclusion, while closed circles indicate inclusion.