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The image shows a graph of a linear function on a grid, and the question is asking to identify the inequality that best represents the **domain** of the part of the function shown. The domain refers to the set of all possible values for \( x \), which is the horizontal axis (independent variable).

Upon examining the graph, we see that the line segment is bounded horizontally between two \( x \)-values. From the grid:

- The left endpoint of the line segment is at \( x = -9 \).
- The right endpoint of the line segment is at \( x = 2 \).

This means that the domain of the function is all values of \( x \) between \( -9 \) and \( 2 \), inclusive of the endpoints.

Thus, the correct inequality representing the domain of the function is:

\[
-9 \leq x \leq 2
\]

This matches the inequality given in the second blue option: **\( -9 \leq x \leq 2 \)**.

Would you like a detailed explanation of the solution or further clarifications?

Here are 5 additional related questions you may want to explore:
1. What is the range of the given linear function?
2. How do you find the equation of a line given two points?
3. How can you determine if a function is linear based on its graph?
4. What is the relationship between slope and the steepness of a line?
5. How do we determine the intercepts of a linear function from its graph?

**Tip**: When analyzing functions from a graph, always separate the domain (horizontal extent) from the range (vertical extent) to understand the function's behavior fully.

The graph of part of a linear function g is shown in the grid. Which inequality best represents the domain of the part shown?

Learn how to determine the domain of a linear function from its graph. This example focuses on identifying the inequality that represents the domain of a function segment, ideal for students in Grades 8-10.

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