The graph shows a linear function with a segment between two points: $(-4, 3)$ and $(1, -4)$. The question asks for the range of this part of the linear function.

Range of a Function:

The range of a function is the set of all possible $y$-values (outputs) that the function can take. To find the range from the graph, we examine the $y$-coordinates of the segment's endpoints.

From the graph:

• The highest point has a $y$-value of $3$ (from $(-4, 3)$).
• The lowest point has a $y$-value of $-4$ (from $(1, -4)$).

Therefore, the range of the function is the set of $y$-values between $-4$ and $3$.

Answer:

The range is the set of all real numbers from -4 to 3.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this:

1. How would you find the domain of this function?
2. How do you determine the slope of this linear function?
3. What would the range be if the line extended indefinitely in both directions?
4. How do the endpoints of the function affect the range?
5. How would the graph change if the line segment were steeper or shallower?

Tip: When determining the range of a graph, always focus on the vertical span of the curve or line.