Final answer:
The equation is y = (1/3)(x + 1)^3 - 2.
Step-by-step explanation:
The equation that shows the transformations of a cubic function that is shrunk horizontally by a factor of 3 and is shifted 1 unit to the left and 2 units down is: y = (1/3)(x + 1)^3 - 2
This equation represents a horizontal compression by a factor of 3, a shift of 1 unit to the left, and a downward shift of 2 units.
The original cubic function y = x^3 has been transformed according to these operations.