Question

determine the amplitude and period of the following function. then graph the function. y = -7 sin 4πx the amplitude is 7. the period (type an exact answer using π as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the period formula for sine function

For a sine function of the form \( y = A\sin(Bx) \), the period \( P \) is given by \( P=\frac{2\pi}{|B|} \).
In the function \( y = - 7\sin(4\pi x) \), we identify \( B = 4\pi \).

Step2: Calculate the period

Substitute \( B = 4\pi \) into the period formula:
\( P=\frac{2\pi}{|4\pi|}=\frac{2\pi}{4\pi}=\frac{1}{2} \)

Answer:

\(\frac{1}{2}\)