Final answer:
To find the domain of an image rotated 270 degrees counter-clockwise with a given range, swap and negate the y-coordinates to simulate a 90-degree clockwise rotation. The domain of the rotated image is (4,3), (1, 1), (7,6).
Step-by-step explanation:
To identify the domain of an image that has been rotated 270 degrees counter-clockwise about the origin with the given range, we must map each point of the range onto the corresponding domain through the rotation. A rotation of 270 degrees counter-clockwise is equivalent to a rotation of 90 degrees clockwise.
To perform a 90-degree clockwise rotation, you can swap the x and y coordinates of each point and then change the sign of the new y-coordinate. Given the range (3,-4), (1, -1), (6, -7), after the rotation the new coordinates will correspond to:
- (3,-4) becomes (4,3)
- (1,-1) becomes (1,1)
- (6,-7) becomes (7,6)
Therefore, the domain of the rotated image is (4,3), (1, 1), (7,6).