To determine the inequality that best represents the domain of the part of the function shown, let's first analyze the graph.

Analysis:

• The graph shows a linear function with a defined segment. The segment starts at $x = -9$ and ends at $x = 2$.
• Therefore, the domain of this function is the set of $x$-values for which the function is defined, which is from $x = -9$ to $x = 2$.

Thus, the correct inequality that represents the domain is:

$-9 \leq x \leq 2$

This matches the option: $-9 \leq x \leq 2$.

Would you like more details on how to interpret the graph, or do you have any further questions?

Here are 5 related questions you could explore:

1. How would you describe the range of this function?
2. What is the slope of the linear function segment shown?
3. How do you find the equation of the line based on the points shown?
4. What are the key differences between domain and range?
5. How do you solve inequalities involving absolute values?

Tip:

When determining the domain of a function from its graph, focus on the extent of the $x$-axis values that the graph covers.