Final answer:
The equation for the function g(x), which is the result of translating the graph of f(x) = 3^x six units to the right, is g(x) = 3^(x-6), corresponding to option c in the question.
Step-by-step explanation:
The translation of the graph of a function involves shifting the graph in different directions without changing its shape. When we talk about translating the graph of f(x) = 3x six units to the right, we are referring to a horizontal shift of the graph. This is accomplished by subtracting the number of units we want to shift from the variable x in the function's equation. The new function, g(x), will thus be represented by the equation g(x) = 3x-6.
The correct option for the equation of g(x), which is the result of translating the graph of f(x) = 3x six units to the right is c. g(x) = 3x-6.