How can a transformation be represented in function notation?

The representation of a transformation in function notation should clearly indicate how points in the original space are altered to yield points in the transformed space. The correct answer uses the notation (T(x, y) = (x', y')) to express that the transformation (T) takes an input point ((x, y)) and maps it to a new point ((x', y')).

This notation is precise and unambiguous, as it indicates that the outputs (x') and (y') are likely functions of the inputs (x) and (y), which is the core concept of function notation in mathematics. It allows for flexibility, letting one define various transformations based on how (x') and (y') are determined from (x) and (y).

In contrast, the other options represent transformations in varying ways but do not fit the correct criteria of function notation as cleanly. For instance, some explicitly show the relationships between the original and transformed coordinates—like options A and D—but they do not serve to generalize the concept as effectively as option C does. Option B indicates that there is no transformation taking place, which does not align with the concept of a transformation.