the black graph is y = sin x. choose the equation for the red graph.\ny = sin(x) - 1\ny = sin(x) + 1\ny =…

Answer:

A. $y = \sin(x)-1$

Explanation:

Step1: Analyze vertical - shift

The point $(0,0)$ on $y = \sin(x)$ moves to $(0, - 1)$ on the red graph. This indicates a vertical shift down by 1 unit. The general form of a vertical - shifted sine function is $y=\sin(x)+k$, where $k$ is the vertical shift. When $k=-1$, the function is $y = \sin(x)-1$.

Step2: Check other options

For $y=\sin(x) + 1$, the graph of $y = \sin(x)$ would shift up by 1 unit. For $y=\sin(x+\pi)=-\sin(x)$ and $y=\sin(x - \pi)=-\sin(x)$, these are phase - shifted and reflected versions of $y = \sin(x)$ and do not account for the vertical shift observed. So the equation of the red graph is $y=\sin(x)-1$.