Sketch on the same diagram the graphs of $y=\left| x-1 \right|$ and $y={{x}^{2}}-3$. Hence solve the

Question

Sketch on the same diagram the graphs of $y=\left| x-1 \right|$ and $y={{x}^{2}}-3$. Hence solve the inequality $\left| x-1 \right|[3] A curve $C$ has equation $y=\frac{2{{x}^{2}}+x+a}{x}$. For $a>1$, sketch $C$, labelling clearly the equations of the asymptotes and the coordinates of the stationary points in terms of $a$ where appropriate. [4] Given that the solution set of the inequality $\frac{2{{x}^{2}}+x+a}{x}\le 0$ is $\left( -\infty ,0 \right)$, deduce the set of values of $a$. [2]

Accepted Answer

$x 2$; OA: $y=2x+1$, VA: $x=0$; $a \geq \dfrac{1}{8}$

2022 RI Promo Q7

2022 RI Promo Q7

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