find the amplitude (if one exists), period, and phase shift of the function. graph the function. be sure to…

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 = 4sin(pi x + 1)-4 ) a. the amplitude is (simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fractions for any numbers in the expression.) b. the function does not have an amplitude. what is the period? (simplify your answer. type an exact answer, using ( pi ) 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 ( pi ) as needed. use integers or fractions for any numbers in the expression.) use the graphing tool to graph the function.

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 = 4sin(pi x + 1)-4 ) a. the amplitude is (simplify your answer. type an exact answer, using ( pi ) as needed. use integers or fractions for any numbers in the expression.) b. the function does not have an amplitude. what is the period? (simplify your answer. type an exact answer, using ( pi ) 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 ( pi ) as needed. use integers or fractions for any numbers in the expression.) use the graphing tool to graph the function.

Answer

Explanation:

Step1: Find the amplitude

For a sine function (y = A\sin(Bx - C)+D), the amplitude is (|A|). In the function (y = 4\sin(\pi x + 1)-4), (A = 4). So the amplitude is (|4|=4).

Step2: Find the period

The formula for the period of a sine function (y = A\sin(Bx - C)+D) is (T=\frac{2\pi}{|B|}). Here (B=\pi), so (T = \frac{2\pi}{\pi}=2).

Step3: Find the phase shift

The formula for the phase shift of a sine function (y = A\sin(Bx - C)+D) is (\text{Phase Shift}=\frac{C}{B}). Rewrite (y = 4\sin(\pi x + 1)-4) as (y = 4\sin(\pi(x+\frac{1}{\pi}))-4), so (C=- 1) (in the form (y = A\sin(Bx - C)+D)), (B = \pi). Then the phase shift is (\frac{-1}{\pi}=-\frac{1}{\pi}).

Answer:

The amplitude is (4). The period is (2). The phase shift is (-\frac{1}{\pi}).