Final answer:
The function f(x,y) = (-x,-y) represents a 180 degree rotation around the origin, moving points to the opposite quadrant on the coordinate plane.
Step-by-step explanation:
The transformation described by the function f(x,y) = (-x,-y) corresponds to a 180 degree rotation around the origin. When both the x and y coordinates of a point are negated, the point is rotated by 180 degrees in the coordinate plane. This means that every point on the plane will be in the exact opposite quadrant after the transformation. It is not a reflection over the line y=x, a 90 degree rotation, or a reflection over the y-axis.
To visualize this, imagine a point in the first quadrant (positive x and y values). Applying the function, it will move to the third quadrant, reflecting across both axes, which is exactly what happens during a 180 degree rotation. This kind of transformation maintains the relative positions of all points as if they have been rotated half a turn around the center point.