Graph the following function over a two perhod interval Give the period and the amplitude \[ y=\frac{1}{4} \cos \frac{\pi}{4} x \]

Step 1 ：The amplitude of a cosine function is the absolute value of the coefficient of the cosine term. In this case, the coefficient of the cosine term is \(\frac{1}{4}\), so the amplitude is \(\frac{1}{4}\).

Step 2 ：The period of a cosine function is given by \(\frac{2\pi}{|B|}\), where \(B\) is the coefficient of \(x\) in the argument of the cosine function. In this case, \(B = \frac{\pi}{4}\), so the period is \(\frac{2\pi}{|\frac{\pi}{4}|} = 8\).

Step 3 ：To graph the function, we generate a range of x-values from 0 to 16 (which is two periods of the function), calculate the corresponding y-values using the function, and then plot the points.

Step 4 ：The graph of the function \(y=\frac{1}{4} \cos \frac{\pi}{4} x\) over a two period interval has been plotted successfully.

Step 5 ：Final Answer: The amplitude of the function is \(\boxed{\frac{1}{4}}\) and the period is \(\boxed{8}\).