https://file.aiquickdraw.com/mathbot/file/17274564235902b2sqn6a.jpg

The graph you provided shows a segment of a linear function, and the task is to find the range of this linear function based on the portion of the graph shown.

### Step 1: Identify the vertical extent of the graph (range)
The **range** refers to the set of all possible *y*-values that the function takes.

1. **Upper bound**: The highest point on the line has a y-coordinate of **3**, as shown by the solid dot at the point (-2, 3).
2. **Lower bound**: The lowest point on the line has a y-coordinate of **-4**, as shown by the open circle at the point (2, -4).

Since the solid dot at \((-2, 3)\) means that the function includes \( y = 3 \), and the open circle at \((2, -4)\) indicates that \( y = -4 \) is **not included**, we can write the range as:

\[
\boxed{ \text{Range: } [-4, 3]}
\]

### Step 2: Confirm with the given choices
According to the image, the range should be stated as:

"The range is the set of all real numbers **greater than or equal to** \( -4 \) and **less than or equal to** \( 3 \)."

- So, the correct selections would be:
  - **Greater than or equal to** \(-4\)
  - **Less than or equal to** \(3\)

Would you like further details on how ranges are determined for different types of functions? Also, feel free to ask any questions.

### 5 Related Questions:
1. How do you determine the range for a quadratic function?
2. What is the difference between range and domain in functions?
3. How do you find the slope of a linear function from a graph?
4. What happens to the range if a graph has no solid or open dots?
5. How do you express the range in interval notation for more complex functions?

**Tip:** Always pay close attention to open and closed circles on graphs—they tell you whether to include or exclude certain values in the range.

What is the range of the part of the linear function shown?

This problem involves identifying the range of a linear function by analyzing a graph. The range is the set of all real numbers from -4 to 3 based on the graph's vertical extent. The problem introduces key concepts like the range and function values, suitable for students in Grades 8-10.

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