Let's analyze the graph of the function $g$ and determine its domain and range.

Domain:

The domain of a function is the set of all possible input values (or $x$-values) that the function can take.

From the graph:

• The graph starts at $x = -2$ and ends at $x = 4$.
• It includes the endpoints, as there are closed circles at $x = -2$ and $x = 4$.

Thus, the domain is: $[-2, 4]$

Range:

The range of a function is the set of all possible output values (or $y$-values) that the function can produce.

From the graph:

• The lowest point is at $y = -2$, and the highest point is at $y = 4$.
• Both endpoints are included in the graph.

Thus, the range is: $[-2, 4]$

Both the domain and the range of the function $g$ are written in interval notation as $[-2, 4]$.

Would you like any further details or clarifications?

Here are 5 related questions:

1. How do you determine the domain and range of a piecewise function?
2. What happens to the domain and range when the graph has open endpoints?
3. How would the domain change if there were vertical asymptotes in the graph?
4. Can a function have multiple disjoint intervals for its range?
5. What is the difference between continuous and discrete domains?

Tip: To determine the domain, always focus on the $x$-axis; for the range, focus on the $y$-axis of the graph.