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 $[0, 2]$