graph the function f(x) = sin(x) + 1.

Explanation:

Step1: Recall properties of y = sin(x)

The function $y = \sin(x)$ has an amplitude of 1, a period of $2\pi$, and it oscillates between - 1 and 1. Its key - points in one period $[0,2\pi]$ are $(0,0),(\frac{\pi}{2},1),(\pi,0),(\frac{3\pi}{2}, - 1),(2\pi,0)$.

Step2: Analyze the transformation of $y=\sin(x)+1$

The function $y = \sin(x)+1$ is a vertical shift of the function $y=\sin(x)$ upwards by 1 unit. So the key - points of $y = \sin(x)+1$ in the period $[0,2\pi]$ are obtained by adding 1 to the y - coordinates of the key - points of $y=\sin(x)$. They are $(0,1),(\frac{\pi}{2},2),(\pi,1),(\frac{3\pi}{2},0),(2\pi,1)$.

Step3: Plot the key - points

Plot the key - points $(0,1),(\frac{\pi}{2},2),(\pi,1),(\frac{3\pi}{2},0),(2\pi,1)$ on the given coordinate grid.

Step4: Sketch the curve

Connect the plotted points with a smooth curve. Since the period of $y = \sin(x)+1$ is $2\pi$, repeat the pattern for other intervals of $x$.

Answer:

Plot the points $(0,1),(\frac{\pi}{2},2),(\pi,1),(\frac{3\pi}{2},0),(2\pi,1)$ and connect them with a smooth curve, repeating the pattern for other $x$ - values.