SAJC Functions Tutorial Q3

It is given that \(\mathrm{f}\left( x \right)=\left\{ \begin{matrix} \sqrt{x} & \mathrm{for }\!\!~\!\!\mathrm{ }\,\,\,\,\,0\le x\le 1, \\ -\frac{1}{2}x+\frac{3}{2} & \mathrm{for }\!\!~\!\!\mathrm{ }\!\!~\!\!\mathrm{ }\,\,\,\,\,1<x\le 3, \\ \end{matrix} \right.\) and that \(\mathrm{f}\left( x \right)=\mathrm{f}\left( x+3 \right)\) for all real values of \(x\).

1. Sketch the graph of \(y=\mathrm{f}\left( x \right)\) for \(-3\le x\le 5\).[3]
2. Hence find the value of \(\displaystyle\displaystyle \displaystyle\int_{-3}^{5}{\mathrm{f}\left( x \right)\,\mathrm{d}x}\).[2]