To determine the correct function mapping for a 90-degree counterclockwise rotation about the origin, we can analyze how the coordinates of a point \((x, y)\) change under this transformation.
When a point \((x, y)\) is rotated 90 degrees counterclockwise, the new coordinates can be calculated as follows:
- The \(x\) coordinate becomes the negative of the original \(y\) coordinate.
- The \(y\) coordinate becomes the original \(x\) coordinate.
Therefore, the transformation can be represented as: \[ (x, y) \rightarrow (-y, x) \]
This corresponds to Option #2: \[ Option #2: (x,y) \rightarrow (-y,x) \]
Thus, the correct option is 2.