Question

Part of a line is graphed at (2, 1) and (6, -3). Which inequalities could describe the domain and range?
a. Domain:\ 2<x<6 Range:\ 2<y<6
b. Domain:\ 2<x\le6 Range:\ -3\le y<1
c. Domain:\ 2\le x<6\ \ Range:\ y<1
d. Domain:\ x\ge2 Range:\ -3<y\le1

Answer 1

To determine which inequalities describe the domain and range of the line segment defined by the points (2, 1) and (6, -3), we need to analyze the coordinates of these points.

1. **Domain**: The x-coordinates of the points are 2 and 6. Therefore, the domain of the line segment includes all x-values from 2 to 6, which can be expressed as:
- \(2 \leq x \leq 6\) or \(2 < x < 6\)

2. **Range**: The y-coordinates of the points are 1 and -3. Because the y-values go from 1 to -3, the range of the line segment includes all y-values from -3 (the lowest) to 1 (the highest). This can be expressed as:
- \(-3 \leq y \leq 1\) or \(-3 < y < 1\)

Analyzing the given options:

a. **Domain:** \(2 < x < 6\) **Range:** \(2 < y < 6\)
- Incorrect. The range does not include values above 1.

b. **Domain:** \(2 < x \le 6\) **Range:** \(-3 \leq y < 1\)
- Correct. Covers the appropriate domain and range values.

c. **Domain:** \(2 \le x < 6\) **Range:** \(y < 1\)
- Incorrect. The range should include the lower bound of -3.

d. **Domain:** \(x \ge 2\) **Range:** \(-3 < y \le 1\)
- Incorrect. The domain should be limited to \(x \leq 6\).

The correct option that describes the domain and range of the line segment defined by the points (2, 1) and (6, -3) is:

**b. Domain:** \(2 < x \le 6\) **Range:** \(-3 \le y < 1\)