Part of a line is graphed. Which
inequalities could describe the
domain and range?
Domain: 2 < x < 6 Range: 2 < y < 6
Domain: 2 < x ≤ 6
Range: −3 ≤ y < 1
Domain: 2 ≤ x < 6 Range: y < 1
Domain: x ≥ 2
Range: −3 < y ≤ 1
Domain: 2 < x ≤ 6
Range: −3 ≤ y < 1
The domain and range of part of a line are given.
`x>0`
`y>4`
Which graph could represent this part of the line graph?
Based on the given inequalities, the graph representing this part of the line would include all points where x is greater than 0 and y is greater than 4. It would be a line in the first quadrant of the coordinate plane, with a vertical asymptote at x=0 and a horizontal asymptote at y=4. The graph would include all points to the right of the y-axis and above the line y=4.
To determine which inequalities could describe the domain and range for a given graphed line, we need to understand how the domain and range are represented on a graph.
Domain represents the set of all possible x-values or inputs for the function. On a graph, it is the range of the x-values shown.
Range represents the set of all possible y-values or outputs for the function. On a graph, it is the range of the y-values shown.
In the given options:
Option 1: Domain: 2 < x < 6, Range: 2 < y < 6
This option states that the domain of x-values lies between 2 and 6, and the range of the y-values lies between 2 and 6. Therefore, this option could describe the domain and range.
Option 2: Domain: 2 < x ≤ 6, Range: −3 ≤ y < 1
This option states that the domain of x-values lies between 2 and 6 (inclusive of 6), and the range of the y-values lies between -3 and 1. Therefore, this option could describe the domain and range.
Option 3: Domain: 2 ≤ x < 6, Range: y < 1
This option states that the domain of x-values lies between 2 (inclusive) and 6, and the range of the y-values is any value less than 1. Since the range has no upper limit specified, this option does not completely describe the range.
Option 4: Domain: x ≥ 2, Range: −3 < y ≤ 1
This option states that the domain of x-values is any value greater than or equal to 2, and the range of the y-values lies between -3 (exclusive) and 1 (inclusive). Therefore, this option could describe the domain and range.
Based on the given options, options 1, 2, and 4 could describe the domain and range of the graphed line.