The curve $C$ has equation $y=\frac{{{x}^{2}}-3x+3}{1-x}$. Sketch $C$, stating the coordinates

Question

The curve $C$ has equation $y=\frac{{{x}^{2}}-3x+3}{1-x}$. Sketch $C$, stating the coordinates of any turning points and points of intersection with the axes, and the equations of any asymptotes.[3] Determine the set of exact values of $k$ such that $C$ and the line $y=kx$ has two points of intersection for all real values of $x$.[3]

Accepted Answer

(a) Asymptotes: $y=2-x$, $x=1$ (b) $\left\{ k\in \mathbb{R}:k3+2\sqrt{3},k
e -1 ight\}$

2023 DHS P1 Q2

2023 DHS P1 Q2

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