Sketch the curve with equation $y=\left| \frac{\alpha x}{x+1} \right|$, where $\alpha $ is

Question

Sketch the curve with equation $y=\left| \frac{\alpha x}{x+1} \right|$, where $\alpha $ is a positive constant, stating the equations of the asymptotes. On the same diagram, sketch the line with equation $y=\alpha x-2$.[3] Solve the inequality $\left| \frac{\alpha x}{x+1} \right|\ge \alpha x-2$, giving your answers in term of $\alpha $.[3]

Accepted Answer

(i) Asymptotes $x=-1$ and $y=\alpha$ (ii) $x\leq\dfrac{1+\sqrt{1+2\alpha}}\alpha$, $x\neq-1$

2019 TJC Promo Q1

2019 TJC Promo Q1

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