Characterizing S-Measurable Functions on $\mathbb{R}$ with Respect to a Simple $\sigma$-Algebra

Let S={$\varnothing $ ,(-$\infty $ ,0), ([0,+$\infty $ ), $\mathbb{R} $ }(wich is a $\sigma $ -algebra on $\mathbb{R}$), then a function f:$\mathbb{R} $ -> $\mathbb{R}$ is S- measurable if and only if f is constant on (-$\infty $ ,0) and if is constant on ([0,+$\infty $ )