2019 NJC P2 Q1

It is given that

\(\mathrm{f}\left( x \right)=\left\{ \begin{matrix} & ax,\mathrm{for }0\le x<2, \\ & \frac{12a}{x}-4a,\mathrm{for }2\le x<3, \\ \end{matrix} \right.\)

where \(a\) is a positive constant and that \(\mathrm{f}\left( x \right)=\mathrm{f}\left( x+3 \right)\) for all real values of \(x\).

1. Find the exact value of \(\mathrm{f}\left( \frac{44}{3} \right)\) in terms of \(a\).[2]
2. Sketch the graph of \(y=\mathrm{f}\left( x \right)\) for \(-3\le x\le 3\), indicating clearly the coordinates of the maximum points and axial intercepts.[3]
3. Find \(\displaystyle\displaystyle \displaystyle\int_{-2}^{2}{\mathrm{f}\left( x \right)\,}\mathrm{d}x\) in terms of \(a\), leaving your answer in the exact form.[3]