https://file.aiquickdraw.com/mathbot/file/1727210017928mov5z39c.jpg

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).

Write an inequality to represent the range of the part of the linear function shown in the graph.

Learn how to write an inequality to represent the range of a linear function. This problem involves understanding the graph of a linear equation and identifying the correct range in inequality notation. Suitable for students in Grades 8-10.

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