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.
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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 \(2 < x < 6\)
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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: \(-3 \le y < 1\)
2 answers