2026 CJC Promo Q8
2026 CJC Promo Q8
Junior College 1
8 marks
Promo
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.
Solution:
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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 \(x=-1,x=2,y=0\).
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