Question

what is the period of the function y = 1/4 cos(π/4 x)? (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) what is the amplitude of the function y = 1/4 cos(π/4 x)? (type an integer or a simplified fraction.) graph the function y = 1/4 cos(π/4 x). choose the correct graph below. a. graph image b. graph image c. graph image d. graph image

Explanation:

Step1: Recall amplitude formula

For a cosine - type function \(y = A\cos(Bx - C)+D\), the amplitude is given by \(|A|\). For the function \(y=\frac{1}{4}\cos(\frac{\pi}{4}x)\), \(A = \frac{1}{4}\), so the amplitude \(|A|=\frac{1}{4}\).

Step2: Recall period formula

The period of a cosine - type function \(y = A\cos(Bx - C)+D\) is \(T=\frac{2\pi}{|B|}\). For the function \(y=\frac{1}{4}\cos(\frac{\pi}{4}x)\), \(B=\frac{\pi}{4}\). Then \(T=\frac{2\pi}{\frac{\pi}{4}}\).

Step3: Calculate the period

\(T=\frac{2\pi}{\frac{\pi}{4}}=2\pi\times\frac{4}{\pi}=8\).

Answer:

Amplitude: \(\frac{1}{4}\)
Period: \(8\)