graph y = 1/2 sin x. first choose the appropriate starting graph from the ones below. then transform it to…

Explanation:

Step1: Identify the base - function

The base - function for $y = \frac{1}{2}\sin x$ is $y=\sin x$. The graph of $y = \sin x$ has an amplitude of 1, a period of $2\pi$, it passes through the points $(0,0)$, $(\frac{\pi}{2},1)$, $(\pi,0)$, $(\frac{3\pi}{2}, - 1)$ and $(2\pi,0)$.

Step2: Analyze the transformation

The function $y=\frac{1}{2}\sin x$ is a vertical compression of the function $y = \sin x$ by a factor of $\frac{1}{2}$. For any $x$ - value, the $y$ - value of $y=\frac{1}{2}\sin x$ is half of the $y$ - value of $y=\sin x$. So the amplitude of $y=\frac{1}{2}\sin x$ is $\frac{1}{2}$, and it passes through the points $(0,0)$, $(\frac{\pi}{2},\frac{1}{2})$, $(\pi,0)$, $(\frac{3\pi}{2},-\frac{1}{2})$ and $(2\pi,0)$.

Answer:

First, choose the graph of $y = \sin x$ (the standard sine - wave with amplitude 1). Then, vertically compress this graph by a factor of $\frac{1}{2}$ to get the graph of $y=\frac{1}{2}\sin x$.