Using translation concepts, it is found that the transformed image of (5,-4) after the composition will be given by:
D.) (-6, 6)
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, first the image is rotated 180º around the origin, hence:
(x,y) -> (-x, -y), then:
(5,-4) -> (-5, 4).
Then, T(-1,2) means that:
(x,y) -> (x - 1, y + 2).
Then:
(-5,4) -> (-5 -1, 4 + 2) -> (-6,6)
Hence option D is correct.
More can be learned about translation concepts at https://brainly.com/question/4521517
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