$f\left(x\right)=\left\{\begin{array}{l}{x}^2,x\ge 1\\ -\frac{1}{2}x,x<1\end{array}\right.$

Domain $\left\{x\in \mathrm{ℝ}\right\}$,  Range $\left\{y\in \mathrm{ℝ},y>-\frac{1}{2}\right\}$