Sketch the curve with equation $y=\left|\dfrac{2x-4}{x-1}\right|$, stating the equations of any as

Question

Sketch the curve with equation $y=\left|\dfrac{2x-4}{x-1}\right|$, stating the equations of any asymptotes. On the same diagram, sketch the line with equation $y=x$.[3] Hence, solve the inequality $\left|\dfrac{2x-4}{x-1}\right|\geq x$, leaving your answer in exact form.[3]

Accepted Answer

(a) Asymptotes $x=1,\ y=2$; intercepts $(0,4),(2,0)$. (b) $x<1$ or $1<x\leq\dfrac{\sqrt{17}-1}{2}$.

2026 HCI Promo Q2

2026 HCI Promo Q2

Solution:

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