2024 JPJC Promo Q8
2024 JPJC Promo Q8
9 marks
- The diagram below shows the graph of \(y = \mathrm{f}(x)\). The curve passes through the points \(A(-a,0)\) and \(B(0,-a)\) and has a minimum point at \(C(2a,-2a)\), where \(a > 0\). The lines \(x = -2a\) and \(y = -a\) are asymptotes of the curve.
On separate diagrams, sketch the graph of- \(y = \mathrm{f}(x-a) + a\),[3]
- \(y = \frac{1}{\mathrm{f}(x)}\),[3]
- The curve whose equation is \(y = \sin x\), undergoes in succession, the following transformations:
\(\mathbf{A}\): A translation by \(\pi\) units in the negative \(x\)-direction.
\(\mathbf{B}\): A scaling parallel to the \(x\)-axis by a factor of \(3\).
\(\mathbf{C}\): A translation by \(2\) units in the positive \(y\)-direction.
Find the equation of the resulting curve.[3]
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Answer:(a)(i) Asymptotes \(x=-a\), \(y=0\); points \((0,a)\), \((a,0)\), \((3a,-a)\). (ii) Asymptotes \(x=-a\), \(y=-1/a\); open point \((-2a,0)\); \(y\)-intercept \((0,-1/a)\); maximum \((2a,-1/(2a))\). (b) \(y=2-\sin(x/3)\).
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