2019 NJC P2 Q1
It is given that
$\text{f}\left( x \right)=\left\{ \begin{matrix}
& ax,\text{for }0\le x<2, \\
& \frac{12a}{x}-4a,\text{for }2\le x<3, \\
\end{matrix} \right.$
where $a$ is a positive constant and that $\text{f}\left( x \right)=\text{f}\left( x+3 \right)$ for all real values of $x$.
(i)
Find the exact value of $\text{f}\left( \frac{44}{3} \right)$ in terms of $a$.
[2]
(ii)
Sketch the graph of $y=\text{f}\left( x \right)$ for $-3\le x\le 3$, indicating clearly the coordinates of the maximum points and axial intercepts.
[3]
(iii)
Find $\int_{-2}^{2}{\text{f}\left( x \right)\,}\text{d}x$ in terms of $a$, leaving your answer in the exact form.
[3]
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