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 = 3sin(pi x + 4)-3 ) o 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.) o 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 the function (y = A\sin(Bx - C)+D), the amplitude is (|A|). In the function (y = 3\sin(\pi x + 4)-3), (A = 3). So the amplitude is (|3|=3).
Step2: Find the period
The period of the function (y = A\sin(Bx - C)+D) is given by (T=\frac{2\pi}{|B|}). Here (B=\pi), so (T=\frac{2\pi}{\pi}=2).
Step3: Find the phase - shift
The phase - shift of the function (y = A\sin(Bx - C)+D) is given by (\frac{C}{B}). Rewrite (y = 3\sin(\pi x + 4)-3) as (y = 3\sin(\pi(x+\frac{4}{\pi}))-3), so (C=- 4) (in the form (y = A\sin(Bx - C)+D)), and (B = \pi). The phase - shift is (\frac{-4}{\pi}) (or (x =-\frac{4}{\pi})).
Answer:
A. The amplitude is (3). The period is (2). The phase - shift is (-\frac{4}{\pi}).