2021 SAJC P1 Q2 (a)

A curve has equation \(y=\mathrm{f}(x)\), where

\(\mathrm{f}(x)\left\{ \begin{matrix} 1-3x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-1\le x\le 1, \\ -2-{{\left( x-1 \right)}^{2}}\,\,\,\,\,\,\,\,\,\,1<x\le 2, \\ 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mathrm{otherwise}\mathrm{.} \\ \end{matrix} \right.\)

Sketch the graph of \(y=\mathrm{f}(x)\) for \(-1\le x\le 4\), stating clearly the coordinates of any axial intercepts. State the range of \(\mathrm{f}\).