Final answer:
The amplitude of the function f(x) = cos(-x) + 1 is 1, the period is 2π, the phase shift is 0, and there is a vertical shift of 1.
Step-by-step explanation:
The function given is f(x) = cos(-x) + 1. To determine the amplitude, period, and phase shift of this function, we look at the general form of a sinusoidal function, which is y(x) = A cos(Bx - C) + D. In this function, A is the amplitude, (2π)/B is the period, C/B is the phase shift, and D is the vertical shift.
In the given function, there is no coefficient in front of the cosine function, which means the amplitude A is 1. The coefficient B associated with x inside the cosine function is 1 (since -x can be written as -1×x), and because there is no phase shift (no 'C' value), the phase shift is 0. The period of the cosine function is 2π divided by the absolute value of the coefficient of x, so in this case, it is 2π/1, which simplifies to 2π. Lastly, since there is '+1' outside the cosine function, there is a vertical shift up by 1, but this does not affect the amplitude or period.
Thus, the amplitude of f(x) is 1, the period is 2π, there is no phase shift, and there is a vertical shift of 1.