Let's analyze the graph to find the domain and range of the function $g$.

Domain:

The domain refers to all the possible values of $x$ for which the function is defined.

• The graph starts at $x = -4$ (where the open circle indicates that the function is not defined at $x = -4$) and continues until $x = 5$ (where another open circle indicates that the function is also not defined at $x = 5$).
• Therefore, the domain is all values of $x$ between $-4$ and $5$, excluding $-4$ and $5$.

In interval notation, the domain is: $(-4, 5)$

Range:

The range refers to all the possible values of $y$ that the function can take.

• The graph starts at $y = -4$ (where there is an open circle, so $y = -4$ is not included), and goes up to $y = 5$ (where another open circle indicates that $y = 5$ is not included).
• The function covers all values between $y = -4$ and $y = 5$, but excludes these boundary points.

In interval notation, the range is: $(-4, 5)$

Final Answer:

• Domain: $(-4, 5)$
• Range: $(-4, 5)$

Would you like further details on how interval notation works or have any other questions?

Here are 5 related questions to expand on this:

1. What is the significance of open and closed intervals in functions?
2. How can you determine the domain and range of a function from its algebraic expression?
3. How do you describe the behavior of the function as $x$ approaches the boundaries of the domain?
4. What changes if the boundary points in the graph were closed circles instead of open circles?
5. How would you write the domain and range if the function extended to infinity?

Tip: Always check for open or closed circles on a graph, as they determine whether boundary points are included in the domain and range.