Single Variable Calculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 7

State the domain and range of the following functions.


$\begin{equation} \begin{aligned} y =& 1 + \sin x\\ \text{ domain:} & [-\infty, \infty]\\ \text{ range:} & [0,2] \end{aligned} \end{equation}$


Recall that the range of $y = \sin x$ is $[-1, 1]$


$\begin{equation} \begin{aligned} \text{So }, y =& 1 + \sin x\\ =& 1 + (-1)\\ =& 0\\ y =& 1 + \sin x\\ =& 1 + (1)\\ =& 2 \end{aligned} \end{equation}$




Therefore, the range of $y = 1 + \sin x$ is $[0, 2]$