2026 NJC Promo Q3
2026 NJC Promo Q3
Junior College 1
8 marks
- The diagram below shows the graph with equation \(y=\mathrm{f}(x)\). It has a minimum point at \((-3,2)\) and asymptotes \(x=-2\), \(y=3\) and \(y=0\).Sketch, on separate diagrams, the graphs of
- \(y=\mathrm{f}(\lvert x\rvert)\),
- \(y=\dfrac{1}{\mathrm{f}(x)}\),
indicating the equations of any asymptotes, and the coordinates of any point where the graph crosses the \(x\)-axis and of any turning points.[5] - State a sequence of geometrical transformations that will transform the graph of \(y=x^2\) onto the graph of \(y=-2x^2-4\).[3]
Solution:
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Answer:(a)(i) Asymptote \(y=0\); minimum point \((0,\mathrm{f}(0))\); no \(x\)-intercept. (ii) Asymptote \(y=\dfrac{1}{3}\); maximum point \(\left(-3,\dfrac{1}{2}\right)\); approaches \((-2,0)\), which is excluded. (b) Scale parallel to the \(y\)-axis by factor \(2\), reflect in the \(x\)-axis, translate \(4\) units in the negative \(y\)-direction.
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