Question

find the amplitude (if one exists), period, and phase shift of the function. graph the function. be sure to label key points. show at least two periods. y = 5 sin(3x - π) what is the amplitude? select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the amplitude is 5 (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) b. the function does not have an amplitude. what is the period? 2π/3 (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) what is the phase shift? (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall amplitude formula

For the general form of a sine - wave function $y = A\sin(Bx - C)$, the amplitude is given by $|A|$. In the function $y = 5\sin(3x-\pi)$, $A = 5$, so the amplitude is $|5|=5$.

Step2: Recall period formula

The period of the function $y = A\sin(Bx - C)$ is $T=\frac{2\pi}{|B|}$. Here, $B = 3$, so $T=\frac{2\pi}{3}$.

Step3: Recall phase - shift formula

The phase - shift of the function $y = A\sin(Bx - C)$ is $\frac{C}{B}$. For the function $y = 5\sin(3x-\pi)$, $C=\pi$ and $B = 3$, so the phase - shift is $\frac{\pi}{3}$.

Answer:

Amplitude: A. The amplitude is 5
Period: $\frac{2\pi}{3}$
Phase - shift: $\frac{\pi}{3}$