The curve $C$ has equation $y=\frac{{{x}^{2}}-4x+1}{2x+7}$, $x\in \mathbb{R}$, $x
e -\frac{7}{2}$.

Question

The curve $C$ has equation $y=\frac{{{x}^{2}}-4x+1}{2x+7}$, $x\in \mathbb{R}$, $x
e -\frac{7}{2}$. Without using a calculator, find the set of values of $y$ that $C$ can take. [3] Sketch $C$, stating the equations of any asymptotes, the coordinates of the points where the curve crosses the axes and the coordinates of the turning points. [4] By drawing a suitable graph on the same diagram, solve the inequality $\frac{4x-{{x}^{2}}-1}{2x+7}>\frac{1}{{{\left( x+1 ight)}^{2}}}$. [3]

Accepted Answer

$y \leq \frac{-11-\sqrt{109}}{2}$ or $y \geq \frac{-11+\sqrt{109}}{2}$; $x < -\frac{7}{2}$ or $1.07 < x < 3.52$

2018 CJC P1 Q9

2018 CJC P1 Q9

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