The curve $C$ has equation $y=2+\frac{3a}{x-a}$, where $a$ is a positive constant. Describe fully a

Question

The curve $C$ has equation $y=2+\frac{3a}{x-a}$, where $a$ is a positive constant. Describe fully a sequence of transformations which would transform the curve $y=\frac{1}{x}$ onto the curve $C$. [3] Sketch the graph of $y=\left| 2+\frac{3a}{x-a} \right|$, labelling the equations of the asymptotes and coordinates of the axial intercepts. [3] Use an algebraic method to solve $\left| 2+\frac{3}{x-1} \right|=3$ and state the solution for $\left| 2+\frac{3}{x-1} \right|[4]

Accepted Answer

$\left\{x \in \mathbb{R}: x 4\right\}$

2023 TMJC P1 Q4

2023 TMJC P1 Q4

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