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.