# What is the range of the graph of y = sin x?

The domain of a function $f \left(x\right)$ are all the values of $x$ for which $f \left(x\right)$ is valid.
The range of a function $f \left(x\right)$ are all the values which $f \left(x\right)$ can take on.
$\sin \left(x\right)$ is defined for all real values of $x$, so it's domain is all real numbers.
However, the value of $\sin \left(x\right)$, its range , is restricted to the closed interval [-1, +1]. (Based on definition of $\sin \left(x\right)$.)