The equation for fand the graph of g are given. How do the period and the amplitude of the functions compare? f(x)=2cos((pi )/(2)x) A. The amplitudes are the same, but the period of fis half as long as the period of g. B. The amplitudes are the same, but the period of fis twice as long as the period of g C. The periods are the same, but the amplitude of fishalf as great as the amplitude of g D. The periods are the same, but the amplitude of fis twice as great as the amplitude of g

Question

Answer 1

Since we don't have information about function

, we cannot definitively answer this question. However, based on our calculations for function

, we can say that the amplitude of

is 2 and the period of

is 4.

Answer 2

## Step 1: First, we need to identify the amplitude and period of function

. The general form of a cosine function is \( f(x) = A \cos(Bx) \), where

is the amplitude and

is the period.## Step 2: From the given function \( f(x) = 2 \cos\left(\frac{\pi}{2}x\right) \), we can see that

and

. Therefore, the amplitude of

is 2 and the period of

is

.## Step 3: Without the equation or the graph of function

, we cannot directly compare the amplitude and period of

and

. However, based on the given options, we can make assumptions about the amplitude and period of

and see which option is consistent with our calculations for

.

Question