Question

determine the amplitude and period of the following function without graphing

( y = 8 sin ( pi x ) )

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 ( pi ) as needed. use integers or fractions for any numbers in the expressio

Explanation:

Step1: Recall the formula for amplitude

For a function \(y = A\sin(Bx)\), the amplitude is \(|A|\).
For \(y = 8\sin(\pi x)\), \(A = 8\), so amplitude \(=|8| = 8\).

Step2: Recall the formula for period

For a function \(y = A\sin(Bx)\), the period \(T=\frac{2\pi}{|B|}\).
For \(y = 8\sin(\pi x)\), \(B=\pi\), so \(T=\frac{2\pi}{|\pi|}=2\).

Answer:

The amplitude is \(8\).
The period \(T = 2\).