A curve $C$ has equation $y=\mathrm{f}\left( x \right)$, where the function $\mathrm{f}$ is defined

Question

A curve $C$ has equation $y=\mathrm{f}\left( x ight)$, where the function $\mathrm{f}$ is defined by $\mathrm{f}:x\mapsto \frac{12-3x}{{{x}^{2}}+4x-5},x\in \mathbb{R},x
e -5,x
e 1$. Find algebraically the range of $\mathrm{f}$. [3] Sketch $C$, indicating all essential features. [4] Describe a pair of transformations which transforms the graph of $C$ on to the graph of $y=\frac{9-x}{{{x}^{2}}-6x}$. [2]

Accepted Answer

$R_{\mathrm{f}} = \left(-\infty, -1-\frac{\sqrt{3}}{2}\right] \cup \left[-1+\frac{\sqrt{3}}{2}, \infty\right)$

2019 VJC P1 Q6

2019 VJC P1 Q6

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