Image of a Function

• Definition: The set of actual outputs the function produces when applied to every element of its domain.
• Formally: $\mathrm{Im}(f)=\{f(x)\mid x\in A\}$
• Note: the image is always a subset of the codomain.
• Example: For $f(x)=x^2:\mathbb{R}\to \mathbb{R}$, the image is $[0,\infty )$.