Sketch the curve with equation $y=\frac{2\left| x-3 \right|}{4-x}$, stating the equations of any a

Question

Sketch the curve with equation $y=\frac{2\left| x-3 \right|}{4-x}$, stating the equations of any asymptotes and the coordinates of the points where the curve crosses the axes.[3] Hence, solve the inequality $-4<\frac{2\left| x-3 \right|}{4-x}\le 1$.[3]

Accepted Answer

(i) Asymptotes: $x=4$, $y=2$, and $y=-2$; intercepts: $(0,\frac32)$ and $(3,0)$. (ii) $2\le x\le\frac{10}{3}$ or $x>5$.

2021 EJC Promo Q3

2021 EJC Promo Q3

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