2019 ASRJC Promo Q6
(a)
It is given that
$\text{f}\left( x \right)=\left\{ \begin{matrix}
& 2+\sqrt{9-{{\left( x-3 \right)}^{2}}}\,\,\,\,\,\text{for}\,\,\,\,0<x<6, \\&2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{for}\,\,\,\,\,6\le x\le 12. \\
\end{matrix} \right.$
and that $\text{f}\left( x \right)=\text{f}\left( x+12 \right)$ for all real values of $x$.
(i) Sketch the graph of $y=\text{f}\left( x \right)$ for $-11\le x\le 12$.
[3]
(ii) Find the exact value of $\int_{-9}^{10}{\text{f}\left( x \right)\,\text{d}x}$.
[2]
(b)
The curve $C$ has equation $y=\frac{2{{x}^{2}}+3}{{{x}^{2}}-6}$.
Using an algebraic method, find the set of value of $y$ that $C$ can take.
[3]
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