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.