To determine the domain and range of the function $g$ based on the graph, we need to observe the x- and y-values that the function covers.

Domain:

The domain of a function consists of all the x-values where the function is defined. From the graph, we observe the following:

• The leftmost point is at $x = -5$, with a filled dot indicating that the function includes this value.
• The rightmost point is at $x = 3$, also with a filled dot indicating the function includes this value.

Thus, the domain is the interval: $\boxed{[-5, 3]}$

Range:

The range consists of all the y-values that the function can take. From the graph, we observe:

• The lowest point occurs at $y = -4$, which is included as it's marked by a filled dot.
• The highest point occurs at $y = 4$, also included due to the filled dot.

Therefore, the range is: $\boxed{[-4, 4]}$

Do you have any questions or want further details? Here are five related questions:

1. How do we handle domain and range if the graph has open circles instead of filled dots?
2. What happens to the domain and range when the function has gaps or discontinuities?
3. Can a function have a range that extends to infinity?
4. How do you define the domain of a function given only its equation?
5. What does it mean for a function to be undefined at certain points?

Tip: Always check for filled or open dots on a graph to determine whether endpoints are included in the domain and range.