To address the question, we need to write an inequality that represents the range of the linear function $g(x)$, as depicted in the graph.

Key details:

1. The range refers to the set of possible $y$-values (i.e., outputs) of the function.
2. The graph shows a segment of the line, so the range is bounded by the minimum and maximum $y$-values of the function at the two endpoints.

Steps:

• The line segment starts at the point $(-7, -5)$ and ends at $(-1, 3)$.
• Therefore, the minimum $y$-value of the function is $-5$ and the maximum $y$-value is $3$.

Writing the inequality:

The range of $g(x)$ is between $-5$ and $3$. Therefore, the inequality that describes this range is: $-5 \leq g(x) \leq 3$

Using the provided options:

• The correct inequality would be: $-5 \leq g(x) \leq 3$ However, the closest match based on the provided answer choices would likely involve rearranging the bounds to reflect the available terms.

Let me know if you would like further clarifications, or if you'd like to move on to the next step.

Here are some follow-up questions to consider:

1. What is the difference between the domain and range of a function?
2. How would you describe the slope of the line shown in the graph?
3. What is the equation of the line shown in slope-intercept form $y = mx + b$?
4. How do you determine the domain of a function from a graph?
5. How can inequalities be used to describe intervals on a graph?

Tip: The range of a function refers to all possible output values (y-values), while the domain refers to all possible input values (x-values).