Function and its codomain

Problem

Name a term of a function defined in \(\mathbb{R}\) with the codomain

1. \(W=[2;+\infty[\)

2. \(W=[-2;2]\)

Solution of part a

A possible solution is given by

\[f(x)=x^2 + 2.\]

Solution of part b

An example for a function limited from above and below is the sine function. However, its codomain is given by \(W=[-1;1]\). In order to obtain the required codomain, we multiply with 2. Thus we arrive at a possible solution

\[g(x)=2\sin(x).\]

Both solutions can be graphically represented by Sage and we can check the codomains.