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.