2022 VJC Promo Q8
A curve $C$ has equation $y=\frac{{{x}^{2}}-2x+7}{x-3}$.
(i)
Using an algebraic method, find the range of values that $y$ cannot take. Leave your answer in exact form.
[4]
(ii)
Sketch the curve $C$, stating the equations of any asymptotes and the exact coordinates of any points where $C$ crosses the axes and of any turning points.
[4]
(iii)
By considering a suitable graph, find the range of values of $k$ such that the equation ${{x}^{4}}-2{{x}^{3}}+7{{x}^{2}}=kx-3k$ has exactly one positive root and one negative root.
[2]
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