Question
Part of a line is graphed. Which inequalities could describe the domain and range?
Graph coordinates: (1, 2), ( -3, 6)
A: Domain: 2< x <6 .Range: 2 < y < 6
B: Domain: 2 < x is less than or equal to 6. Range: -3 is less than or equal to y < 1
C: Domain: 2 is less than or equal to x < 6. Range: y < 1
D: Domain: x is greater than or equal to 2. Range: -3 < y is less than or equal to 1.
Graph coordinates: (1, 2), ( -3, 6)
A: Domain: 2< x <6 .Range: 2 < y < 6
B: Domain: 2 < x is less than or equal to 6. Range: -3 is less than or equal to y < 1
C: Domain: 2 is less than or equal to x < 6. Range: y < 1
D: Domain: x is greater than or equal to 2. Range: -3 < y is less than or equal to 1.
Answers
GPT-4o mini
To determine the correct inequalities that describe the domain and range based on the graph coordinates provided: (1, 2) and (-3, 6), we first need to identify the x-coordinates and y-coordinates represented by these points.
For the coordinates:
- Point (1, 2) has x = 1 and y = 2.
- Point (-3, 6) has x = -3 and y = 6.
**Domain:**
The domain is the set of all x-values that the graph covers. The x-values given in our coordinates are 1 and -3. Thus:
- The minimum x-value is -3.
- The maximum x-value is 1.
Therefore, the domain in inequality form is:
\[
-3 \leq x \leq 1
\]
**Range:**
The range is the set of all y-values from the graph. The y-values at our points are 2 and 6. Thus:
- The minimum y-value is 2.
- The maximum y-value is 6.
Therefore, the range in inequality form is:
\[
2 \leq y \leq 6
\]
Now, let's assess each option with this information:
A: **Domain: 2 < x < 6. Range: 2 < y < 6.**
**Not Correct.** The domain starts at -3, not 2, and the range should include its endpoints.
B: **Domain: 2 < x ≤ 6. Range: -3 ≤ y < 1.**
**Not Correct.** The domain is incorrect, should start from -3, and the range does not cover values up to 2.
C: **Domain: 2 ≤ x < 6. Range: y < 1.**
**Not Correct.** The domain is incorrect and does not start from -3.
D: **Domain: x ≥ -3. Range: -3 < y ≤ 6.**
This is the most accurate option provided. The domain encompasses all x-values from -3 onward, and the range includes values starting from -3 up to and including 6.
The correct response is:
**D: Domain: x ≥ -3. Range: -3 < y ≤ 6.**
For the coordinates:
- Point (1, 2) has x = 1 and y = 2.
- Point (-3, 6) has x = -3 and y = 6.
**Domain:**
The domain is the set of all x-values that the graph covers. The x-values given in our coordinates are 1 and -3. Thus:
- The minimum x-value is -3.
- The maximum x-value is 1.
Therefore, the domain in inequality form is:
\[
-3 \leq x \leq 1
\]
**Range:**
The range is the set of all y-values from the graph. The y-values at our points are 2 and 6. Thus:
- The minimum y-value is 2.
- The maximum y-value is 6.
Therefore, the range in inequality form is:
\[
2 \leq y \leq 6
\]
Now, let's assess each option with this information:
A: **Domain: 2 < x < 6. Range: 2 < y < 6.**
**Not Correct.** The domain starts at -3, not 2, and the range should include its endpoints.
B: **Domain: 2 < x ≤ 6. Range: -3 ≤ y < 1.**
**Not Correct.** The domain is incorrect, should start from -3, and the range does not cover values up to 2.
C: **Domain: 2 ≤ x < 6. Range: y < 1.**
**Not Correct.** The domain is incorrect and does not start from -3.
D: **Domain: x ≥ -3. Range: -3 < y ≤ 6.**
This is the most accurate option provided. The domain encompasses all x-values from -3 onward, and the range includes values starting from -3 up to and including 6.
The correct response is:
**D: Domain: x ≥ -3. Range: -3 < y ≤ 6.**