2. $y = 4 cos(x)$\nphase shift: ____________ period: ____________\nvertical shift: ____________ amplitude…

Explanation:

Step1: Recall the general form of cosine function

The general form of a cosine function is (y = A\cos(B(x - C))+D), where (A) is the amplitude, (B) affects the period ((T=\frac{2\pi}{|B|})), (C) is the phase - shift, and (D) is the vertical - shift. For the function (y = 4\cos(x)), we can rewrite it as (y=4\cos(1(x - 0))+0).

Step2: Calculate the phase - shift

Comparing (y = 4\cos(x)) with (y = A\cos(B(x - C))+D), we have (C = 0). So the phase - shift is (0).

Step3: Calculate the period

Using the formula (T=\frac{2\pi}{|B|}), since (B = 1), then (T=\frac{2\pi}{|1|}=2\pi).

Step4: Calculate the vertical - shift

Comparing with the general form (y = A\cos(B(x - C))+D), we have (D = 0). So the vertical - shift is (0).

Step5: Calculate the amplitude

Comparing with the general form (y = A\cos(B(x - C))+D), we have (A = 4). So the amplitude is (4).

Answer:

Phase shift: (0) Period: (2\pi) Vertical shift: (0) Amplitude: (4)