Question

change the equation below to see if your prediction from the last screen was correct.
y = 2 sin 3(x - π) + 1
if we changed the 2 to a 5 in the equation, what would happen to the graph?

Explanation:

Step1: Recall the general form of a sine function

The general form of a sine function is \(y = A\sin(B(x - C))+D\), where \(A\) is the amplitude.

Step2: Analyze the effect of \(A\)

In the original equation \(y = 2\sin(3(x-\pi)) + 1\), \(A = 2\). When we change \(2\) to \(5\), the new amplitude \(A = 5\).
The amplitude of a sine - wave \(y = A\sin(B(x - C))+D\) determines the vertical stretch of the graph. If \(|A|\) increases, the graph is vertically stretched.

Answer:

The graph of the function \(y = 5\sin(3(x-\pi)) + 1\) is a vertical stretch of the graph of \(y = 2\sin(3(x-\pi)) + 1\). The amplitude of the sine function changes from \(2\) to \(5\), so the graph will oscillate between \(y=1 + 5=6\) and \(y=1-5=-4\) (previously it oscillated between \(y = 1+2 = 3\) and \(y=1 - 2=-1\)).