Question

determine the amplitude and period of the following function without graphing.
y = 9 cos(πx)
for the function given, the amplitude is □.
(use integers or fractions for any numbers in the expression.)
for the function given, the period is t = □.
(simplify your answer. type an exact answer, using π as needed. use integers or fracti

Explanation:

Step1: Recall the formula for amplitude

For a function \(y = A\cos(Bx)\), the amplitude is \(|A|\).
In the function \(y = 9\cos(\pi x)\), \(A = 9\). So the amplitude is \(|9|=9\).

Step2: Recall the formula for period

For a function \(y = A\cos(Bx)\), the period \(T=\frac{2\pi}{|B|}\).
In the function \(y = 9\cos(\pi x)\), \(B=\pi\). Then \(T=\frac{2\pi}{|\pi|}\).
Since \(|\pi|=\pi\), we have \(T = 2\).

Answer:

The amplitude is \(9\). The period \(T = 2\).