Final answer:
The transformation from f(x) to g(x) involves a horizontal phase shift of π/16 to the right and a vertical translation of 7 units down.
Step-by-step explanation:
The transformation from f(x) = 6 sin(x-π/8) + 8 to g(x) = 6 sin(x -7π/16 )+1 involves two main changes. First, there is a horizontal shift, which is determined by the change in the phase of the sine function.
The original function has a phase shift of π/8, while the new function has a phase shift of 7π/16, resulting in a phase shift to the right by an additional π/16. Second, there is a vertical translation. The original function is translated 7 units up, as indicated by the constant term changing from +8 in f(x) to +1 in g(x).