## Precalculus (6th Edition) Blitzer

Given $y=2sin\frac{x}{2}+1$, we can identify its period as $p=\frac{2\pi}{1/2}=4\pi$. To graph the function, start from $y=sin(x)$ (green curve), stretch horizontally by a factor of 2, stretch vertically by a factor of 2, then shift 1 unit up to get the red curve for $y=2sin\frac{x}{2}+1$ as shown in the figure.