Given that both $a$ and $b$ are positive constants, on the same diagram, sketch the graphs

Question

Given that both $a$ and $b$ are positive constants, on the same diagram, sketch the graphs of $y=\frac{2}{\left| x-a \right|}$ and $y=b\left| x-a \right|$.[3] Hence, or otherwise, solve the inequality $\frac{2}{\left| x-a \right|}>b\left| x-a \right|$.[3]

Accepted Answer

(a) $\dfrac{2}{|x-a|}$: asymptotes $x=a$, $y=0$; $b|x-a|$: vertex $(a,0)$; intersections $\left(a\pm\sqrt{\dfrac2b},\sqrt{2b}\right)$ (b) $a-\sqrt{\dfrac2b}<x<a$ or $a<x<a+\sqrt{\dfrac2b}$

2022 DHS Promo Q7

2022 DHS Promo Q7

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