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).
