The reciprocals in the first three parts of Exploration Activity are, respectively, `x^-2`, `x^-1/2`, and `x^-3`. In contrast to the last of these, the inverse of the cubing function is the cube root function, `x^(1/3)`. We show the graphs of the cube (black), reciprocal cube (red), and cube root (blue) functions in Figure A4. Observe that the cube and cube root functions are mirror images of each other in the line `y=x`. On the other hand, the reciprocal cube function does not have the shape of either of the others. Its values are big where `x^3` is small, and vice versa.
Figure A4 Graphs of cube (black), reciprocal cube (red), and cube root (blue) functions