Question

find the amplitude (if one exists), label key points. show at least two
y = 2 sin (πx + 3) − 3
a. the amplitude is 2
(simplify your answer. type for any numbers in the exp
b. the function does not have
what is the period?
2
(simplify your answer. type an exa numbers in the expression.)
what is the phase shift?
−\frac{3}{π}
(simplify your answer. type an exa numbers in the expression )
use the graphing tool to graph the
(for any answer boxes shown with the grapher type an exact answer type the word pi symbol π as needed.)
use the given interactions to edit the

Explanation:

Step1: Recall the period formula for sine function

The general form of a sine function is \( y = A\sin(Bx + C) + D \), and the period \( P \) is given by \( P=\frac{2\pi}{|B|} \).

Step2: Identify \( B \) from the given function

For the function \( y = 2\sin(\pi x+ 3)-3 \), we can see that \( B = \pi \).

Step3: Calculate the period

Substitute \( B=\pi \) into the period formula: \( P = \frac{2\pi}{|\pi|} \). Since \( \pi>0 \), \( |\pi|=\pi \), so \( P=\frac{2\pi}{\pi}=2 \).

Answer:

The period of the function \( y = 2\sin(\pi x + 3)-3 \) is \( 2 \).