Final answer:
The image of the point (4,-7) after a reflection over the line y = -x is (7, -4), which involves swapping and negating the original coordinates.
Step-by-step explanation:
The question asks for the image of the point (4,-7) after a reflection over the line xy = -x. This line describes a reflection over the line y = -x, which implies that any point (a, b) after reflection over the line y = -x would become (-b, -a). Applying this to the given point (4, -7), the reflected image would be (7, -4).
Reflections over a line like y = -x can be visualized as flipping the coordinate over the line where the x-coordinate and the y-coordinate are swapped and negated.
For even and odd functions, this reflection characterizes the symmetry related to odd functions, which are symmetric with respect to the origin when reflected over both axes. An even function would be symmetric about the y-axis alone.