Question

change the equation below to see if your prediction from the last screen was correct.
$y = 2\sin3(x - \pi)+1$
if we changed the 1 to a -1 in the equation, what would happen to the graph?

Explanation:

Step1: Recall the transformation rule

For a function \(y = A\sin(B(x - C))+D\), the value of \(D\) represents a vertical shift. If \(D>0\), the graph shifts up by \(D\) units; if \(D < 0\), the graph shifts down by \(|D|\) units.
In the original function \(y = 2\sin3(x-\pi)+1\), \(D = 1\). When we change it to \(y=2\sin3(x - \pi)-1\), the new \(D=- 1\).

Step2: Calculate the vertical shift

The original vertical shift is \(1\) unit up. The new vertical shift is \(1\) unit down. The change in the vertical - shift is \((-1)-1=-2\) units.

Answer:

The graph of the function \(y = 2\sin3(x-\pi)+1\) is shifted down by \(2\) units to get the graph of \(y = 2\sin3(x - \pi)-1\).