Question

predict #1
if we changed the 2 to a 5 in the equation, what would happen to
the graph?
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$y = 2 sin 3 ( x - pi ) + 1$

Explanation:

Step1: Recall the amplitude formula

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 changing \(A\)

In the original equation \(y = 2\sin(3(x-\pi)) + 1\), \(A = 2\). If we change \(2\) to \(5\) (new equation \(y=5\sin(3(x - \pi))+1\)), the amplitude changes. The amplitude determines the vertical stretch of the graph. A larger \(|A|\) means a greater vertical stretch.

Answer:

The graph of the sine function would be vertically stretched. The peaks would be at \(y = 5 + 1=6\) and the troughs at \(y=-5 + 1=-4\) instead of \(y = 2+1 = 3\) and \(y=-2 + 1=-1\) (original amplitude - related values). So the graph becomes taller (more vertically stretched).