Question

change the equation below to see if your prediction from the last screen was correct.
$y = 2\sin3(x - \pi)$
if we changed the 2 to a 5 in the equation, what would happen to the graph?

Explanation:

Step1: Recall the amplitude formula

For a sine function \(y = A\sin(B(x - C))+D\), the amplitude is \(|A|\).

Step2: Analyze the effect of changing \(A\)

In the original function \(y = 2\sin(3(x-\pi))\), \(A = 2\). If we change \(A\) to \(5\) (new function \(y=5\sin(3(x - \pi))\)), since the amplitude is \(|A|\), the amplitude changes from \(|2| = 2\) to \(|5|=5\).

Answer:

The amplitude of the sine - wave graph would increase. The graph would be stretched vertically. The peaks would reach \(y = 5\) and the troughs would reach \(y=-5\) instead of \(y = 2\) and \(y=-2\) respectively.