Final answer:
The amplitude (A) is 8, the period (P) is π, and the phase shift (PS) is 4 units to the right. There is no vertical phase shift, since 10 represents a vertical translation. The correct answer is A = 8, P = π, PS = (4, 10).
Step-by-step explanation:
To determine the amplitude (A), period (P), and phase shift (PS) of the function f(x) = 8sin(2(x - 4)) + 10, we analyze the given function in its standard form f(x) = Asin(B(x - C)) + D.
The amplitude A is the coefficient in front of the sine function, which represents the maximum displacement from the function's midline. In this case, the amplitude is 8.
The period of a sine function is given by P = 2π/B, where B is the coefficient of x within the sine function. For our function, B is 2, thus the period P is π radians.
The phase shift is the horizontal shift of the function along the x-axis, calculated by the value of C in the standard form. The phase shift of this function is 4 units to the right. There is no vertical shift since 10 is the vertical translation, not part of the phase shift.
Therefore, the correct answer is: A = 8, P = π, PS = (4, 10).