To determine which inequalities could describe the domain and range for a part of a line that is graphed, we need to consider the specific intervals for both x (the domain) and y (the range).
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Domain: This refers to the possible values of x. If we have a segment of a line, the x-coordinates will be bound between certain values.
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Range: This indicates the corresponding y-values for the given x-values. A line segment may also be limited vertically, indicating the acceptable y-values.
Let's analyze each option based on typical behavior of line segments:
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Option a) Domain: \(2 < x < 6\), Range: \(2 < y < 6\)
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This suggests both x and y values are bounded; this could describe a segment in the first quadrant if the line is rising.
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Option b) Domain: \(2 < x < 6\), Range: \(-3 < y < 1\)
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This indicates a horizontal line segment between x-values of 2 and 6, but y is limited to values between -3 and 1; this is possible if the line stays below y = 1.
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Option c) Domain: \(2 < x < 6\), Range: \(y < 1\)
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This implies a line segment limited to certain x-values but unrestricted below y=1; also possible if the line is consistently below that level.
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Option d) Domain: \(x > 2\), Range: \(-3 < y < 1\)
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This suggests that the segment starts at x = 2 and extends infinitely to the right, with y constrained between -3 and 1; this could also describe a line segment.
Without more information about the specific part of the line being graphed, all four options might be valid depending on the exact appearance of the line segment. However, if we had to choose the one that best describes a typical segment, a) or b) would likely be the most complete descriptions since they provide bounded intervals for both \(x\) and \(y\).