Range of a function

The range of a function is the set of its possible output values.

For example, for the function $f(x)=x^2$ on the domain of all real numbers ($x\in\mathbb{R}$), the range is the non-negative real numbers, which can be written as $f(x)\ge0$ (or $[0,\infty)$ using interval notation).

The range of the function $f(x)=\sin x$, $x\in\mathbb{R}$ is the real numbers between $-1$ and $1$, that is $-1\le f(x)\le 1$ (or $[-1,1]$ using interval notation).

The domain of the function can affect the range so, for example, the range of the function $g(x)=\sin x$, $x\in\mathbb{R}$, $0<x<\frac{\pi}{2}$ is the real numbers between $0$ and $1$, that is $0<g(x)<1$ (or $(0,1)$ using interval notation).