Part of a line is graphed. Which inequalities could describe the domain and range?

Question

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

Answer 1

To determine which inequalities could describe the domain and range of a graphed line, we need to understand what each inequality represents in terms of the values that \(x\) and \(y\) can take.

1. Domain: \(2 < x < 6\)
   This means \(x\) can take any value between 2 and 6, not including 2 and 6 themselves.

   Range: \(2 < y < 6\)
   This means \(y\) can take any value between 2 and 6, also not including 2 and 6.

2. Domain: \(2 < x ≤ 6\)
   This means \(x\) can take any value greater than 2 and up to and including 6.

   Range: \(-3 ≤ y < 1\)
   This means \(y\) can take any value greater than or equal to -3 but less than 1.

3. Domain: \(2 ≤ x < 6\)
   This means \(x\) can take any value greater than or equal to 2 and up to but not including 6.

   Range: \(y < 1\)
   This means \(y\) can take any value less than 1, without bounds.

4. Domain: \(x ≥ 2\)
   This means \(x\) can take any value greater than or equal to 2 with no upper limit.

   Range: \(-3 < y ≤ 1\)
   This means \(y\) can take any value greater than -3 and up to and including 1.

To determine which of these sets of inequalities might be true, we would typically look at the graph to see where the line is defined along the x-axis (domain) and the corresponding y-values (range).

Without the visual representation of the graph, it’s essential to analyze which set of inequalities is most plausible given common scenarios of linear functions.

Likely Candidates:

• If the line is limited to a small segment between specific values, then option 1 or 2 might be true.
• If the line runs indefinitely to the right (or has no upper limit in the x-direction), option 4 could hold.
• If it has open and closed intervals across the entire graph, option 3 might also hold.

You may need to check the graph specifically for endpoints and behaviors to see how to best match the inequalities with the line's actual plotted values.

Answer 2

The points are (2, 1) and (6, -3)

Answer 3

Given the points (2, 1) and (6, -3), we can analyze the domain and range of the line segment that connects these points.

1. Domain:

The domain consists of the x-values of the endpoints. The points (2, 1) and (6, -3) provide the following x-values:

• The smallest x-value is 2.
• The largest x-value is 6.

Since the endpoints are included in the graph, the correct domain should be:

• \(2 \leq x \leq 6\)

2. Range:

The range consists of the y-values of the endpoints:

• At \(x = 2\), the y-value is 1.
• At \(x = 6\), the y-value is -3.

Thus, we have \(y\) values ranging from -3 to 1. The correct range, considering that the endpoints are included, should be:

• \(-3 \leq y \leq 1\)

Conclusion:

Based on the analysis of the points (2, 1) and (6, -3):

• Domain: \(2 \leq x \leq 6\) (which aligns with Option 3: \(2 \leq x < 6\) but includes 2, so while they are not exactly matching, this is the closest.)
• Range: \(-3 \leq y \leq 1\) (which does not match any of the exact options perfectly.)

Among the provided options:

1. Domain: \(2 < x < 6\) Range: \(2 < y < 6\) — Incorrect
2. Domain: \(2 < x ≤ 6\) Range: \(-3 ≤ y < 1\) — Incorrect (it contains an open interval in the range)
3. Domain: \(2 ≤ x < 6\) Range: \(y < 1\) — Incorrect
4. Domain: \(x ≥ 2\) Range: \(-3 < y ≤ 1\) — Incorrect

Revised Answer Based on the Points Given:

Since none of the provided options reflect the full and correct domain and range based on the points given:

• Correct Domain: \(2 \leq x \leq 6\)
• Correct Range: \(-3 \leq y \leq 1\)

So, none of the options accurately fit the graph of the line connecting the points (2, 1) and (6, -3).