The diagram shows the curve $y=\mathrm f(x)$. The curve has a minimum point at $A(-2,2)$ and a m

Question

The diagram shows the curve $y=\mathrm f(x)$. The curve has a minimum point at $A(-2,2)$ and a maximum point at $B(0,-2)$. The lines $x=-1$, $x=2$ and $y=3$ are the asymptotes to the curve. On separate diagrams, sketch the graphs of $y=2\mathrm f(x-1)$,[2] $y=\dfrac1{\mathrm f(x)}$,[3] $y=\mathrm f'(x)$[3] stating clearly the equation of any asymptotes, and the coordinates of any turning points and axial intercepts where possible.

Accepted Answer

(a) Minimum $(-1,4)$, maximum $(1,-4)$; asymptotes $x=0,x=3,y=6$. (b) Maximum $\left(-2,\dfrac12\right)$, minimum $\left(0,-\dfrac12\right)$; asymptote $y=\dfrac13$; continuous extension through $(-1,0),(2,0)$. (c) Zeros $x=-2,0$; asymptotes $x=-1,x=2,y=0$.

2026 CJC Promo Q8

2026 CJC Promo Q8

Solution:

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