Question

What kind of graphical symmetry do inverses have?

A. Reflective symmetry
B. Rotational symmetry
C. Translational symmetry
D. No symmetry

Answer 1

The graphical symmetry that inverses have is reflective symmetry over the line y = x, where each point on the original function is reflected to a point on its inverse creating a mirror image.

Step-by-step explanation:

In graphical terms, the symmetry exhibited by inverses is reflective symmetry across the line y = x. As the inverse function is graphed, each point (x, y) on the original function is mirrored to the point (y, x) on its inverse. This reflection occurs over the line y = x, effectively interchanging the roles of x and y. Consequently, the resulting graph becomes a precise mirror image of the original function. This symmetrical relationship underscores the fundamental connection between a function and its inverse, emphasizing the reciprocal exchange of input and output values in their graphical representation.