https://file.aiquickdraw.com/mathbot/file/1726495618137oyu1t0zj.jpg

In the given image, the graph of a linear function \( g \) is shown, and we are tasked with finding an inequality that represents the domain of the function. The domain refers to the set of \( x \)-values for which the function is defined.

To solve this, let's analyze the graph:

1. The line segment shown on the graph appears to start at approximately \( x = -4 \) and ends at \( x = 2 \), based on the grid lines. These are the \( x \)-coordinates of the endpoints of the segment.

2. Since the segment includes both endpoints (solid points), the domain consists of all \( x \)-values between \( -4 \) and \( 2 \), inclusive.

This gives us the domain:

\[
-4 \leq x \leq 2
\]

Thus, the inequality that best represents the domain of the part of the function shown is \( -4 \leq x \leq 2 \).

Would you like further details on how to interpret graphs like this or how domains are calculated?

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Here are 5 related questions for further exploration:
1. What is the range of the given function?
2. How can we determine the slope of the linear function shown in the graph?
3. How would the domain change if the endpoints were open circles?
4. How do we write the equation of the linear function from the graph?
5. What is the significance of the domain and range in real-life applications?

**Tip:** When determining the domain of a function from a graph, focus on the horizontal extent of the graph, noting whether endpoints are included or excluded.

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

Find the inequality representing the domain of a linear function graph. The domain is calculated based on the x-values of the graph endpoints. The solution explains how to determine the domain of the function between -4 and 2. Suitable for high school students (Grades 9-12).

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