Question

predict #2
if we changed the 1 to a -1 in the equation, what would happen to
the graph?
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y = 2 sin 3(x - π) + 1

Explanation:

Step1: Analyze the role of the constant term in the sine function

In the general form of a sine function \(y = A\sin(B(x - C))+D\), the constant term \(D\) represents the vertical shift.

Step2: Compare the original and new equations

The original equation is \(y = 2\sin(3(x-\pi)) + 1\), where \(D = 1\). The new equation would be \(y=2\sin(3(x - \pi))-1\), where \(D=- 1\).

Step3: Determine the effect of the change

Since the vertical shift changes from \(1\) to \(-1\), the graph of the sine function will shift downward by \(2\) units (because \(1-(-1)=2\)).

Answer:

The graph of the function \(y = 2\sin(3(x-\pi)) + 1\) is shifted downward by \(2\) units when the \(1\) is changed to \(-1\) in the equation.