The graphs of $y=2|5x-p|$ and $y=qx$, where $p,q0$, intersect at only one point. On a

Question

The graphs of $y=2|5x-p|$ and $y=qx$, where $p,q>0$, intersect at only one point. On a single diagram, sketch the two graphs. State the range of values of $q$. [3] Solve $2|5x-p|<10x$. Deduce the solution set of the inequality $\left|\frac{10}{x}-2p\right|<\frac{10}{x}$. Leave both answers in terms of $p$. [3] The diagram shows a sketch of the curve $y=2\mathrm{f}(-x-1)$. The curve has asymptotes with equation $x=-1$, $x=1$ and $y=0$. The curve has a stationary point of inflexion at $(0,0)$, a maximum point at $(-2,3)$ and cuts the $x$-axis at $(-1.5,0)$. On separate diagrams, sketch the graphs of $y=\frac{1}{2\mathrm{f}(-x-1)}$,[3] $y=\mathrm{f}(x)$, [3] stating clearly the equation of any asymptotes, and the coordinates of any turning points and axial intercepts.

Accepted Answer

(a)(i) (q\ge10) (a)(ii) (x>\dfrac{p}{10}); (0<x<\dfrac{10}{p}) (b) the two requested sketches with stated asymptotes and key points

2025 DHS Promo Q11

2025 DHS Promo Q11

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