# How do you draw the graph of y=1+sinx for 0<=x<2pi?

The graph of $\sin x$ will have its $y$-intercept at $x = 0$. It has an amplitude of $1$, so it will always have a maximum of $y = 1$ and a minimum of $y = - 1$. It first goes up, and then comes back down to reach a minimum, passing through the line $y = 0$, which is in fact the axis of symmetry.
The period of sine is $2 \pi$, that's to say it takes $2 \pi$ units for it to repeat itself.
As for $y = 1 + \sin x$, this is the graph of $y = \sin x$, with the axis of symmetry moved up $1$ unit to $y = 1$. The graph of $y = 1 + \sin x$ is shown in the following image.