Sketch the curve with equation $y=\left| \frac{2x-q}{x-1} \right|$, where $q2$, stating

Question

Sketch the curve with equation $y=\left| \frac{2x-q}{x-1} \right|$, where $q>2$, stating the equations of the asymptotes and the coordinates of the points where the curve meets the axes.[3] Hence, by adding a suitable line on the same diagram in part (a), solve the inequality $\left| \frac{2x-q}{x-1} \right|-2x>0$, giving your answer in terms of $q$.[3]

Accepted Answer

(a) Asymptotes: $x=1$, $y=2$; intercepts: $(0,q)$, $\left(\dfrac q2,0\right)$ (b) $x<1$ or $1<x<\sqrt{\dfrac q2}$

2024 HCI Promo Q4

2024 HCI Promo Q4

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