The curve $C$ has equation $y=\frac{{{x}^{2}}+14x+50}{3\left( x+7 \right)}$, $x\in \mathbb{R}$

Question

The curve $C$ has equation $y=\frac{{{x}^{2}}+14x+50}{3\left( x+7 \right)}$, $x\in \mathbb{R}$, $x\ne -7$. Using an algebraic method, find the set of values that $y$ can take.[5] Find the equation(s) of the asymptotes of $C$.[2] Sketch $C$, labelling clearly the asymptotes, turning point(s) and intersection(s) with the axes, where applicable.[3] Hence, solve the inequality $\left| \frac{{{x}^{2}}+14x+50}{x+7} \right|<3$.[3]

Accepted Answer

(i) $\left\{ x\in \mathbb{R}:y\le -\frac{2}{3}\, \right.$ or $\left. y\ge \frac{2}{3} \right\}$ (ii) $y=\frac{1}{3}\left( x+7 \right)$; $x=-7$ (iv) $-9.62<x<-7.38$ or $-6.62<x<-4.38$

2017 MJC Promo Q10

2017 MJC Promo Q10

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