2025 YIJC P1 Q6
2025 YIJC P1 Q6
Junior College 2
7 marks
The diagram below shows the graph of \(y=\mathrm{f}(x)\). The graph has asymptotes \(y=a+bx\) and \(x=0\), intersects the \(x\)-axis at the point \((c, 0)\) and has a turning point \((d, e)\).
Sketch the following graphs on separate diagrams, labelling the equations of any asymptotes and the coordinates of any points where the graphs cross the axes and of any turning points.
- \(y=3\mathrm{f}(x+c)\),[2]
- \(y=\frac{1}{\mathrm{f}(x)}\),[3]
- \(y=\mathrm{f}'(x)\).[2]
Solution:
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Answer:(a) Asymptotes \(x=-c\), \(y=3a+3b(x+c)\); intercept \((0,0)\), maximum \((d-c,3e)\). (b) Asymptotes \(x=c\), \(y=0\); minimum \((d,\frac{1}{e})\); excluded hole at \((0,0)\), no axis intercepts. (c) Asymptotes \(x=0\), \(y=b\); horizontal-axis intercept \((d,0)\). Sketches shown.
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