A function \(\mathrm{g}(x)\) is given by the rule \(\mathrm{g}(x)=\dfrac{x^2+6}{3-x^2}\).
State the maximal domain of \(\mathrm{g}\).[2]
Find the equations of the asymptotes of \(y=\mathrm{g}(x)\).[4]
Describe a single transformation that maps the graph of \(y=\mathrm{g}(x)\) onto the graph of \(y=\mathrm{h}(x)\), where \(\mathrm{h}(x)=\dfrac{x^2-2x+7}{2+2x-x^2}\).[2]
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Answer:(a) \(\mathbb R\setminus\{-\sqrt3,\sqrt3\}\) (b) \(x=\pm\sqrt3,\ y=-1\) (c) Translation by \(\begin{pmatrix}1\\0\end{pmatrix}\)