Definition of Range (Image)

The range of a function is the smallest set that contains all values it can attain over its domain. The range of $f(x)=\frac{1}{x}$ is not the set of all real numbers because it cannot attain the value of $0$. The range of $f(x)=\sin x$ is not $[-1,0]$, because the function can be more than $0$. However, it would be accurate to say that $f(x)=|x|$ has a range of $[0,\infty)$.