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2026 RVHS P1 Q10

2026 RVHS P1 Q10

Junior College 2
10 marks
  1. The diagram shows the graph of \(y=\mathrm{f}(x)\). The graph intersects the axes at \((2,0)\) and \((0,3)\). It has a turning point at \((-5,6)\) and asymptotes with the equations \(x=4\), \(y=0\) and \(y=3\).
    On separate diagrams, sketch each of the following graphs. For each graph, state the equation of any asymptotes, the coordinates of any points where the curve crosses the axes and the coordinates of any turning points.
    1. \(y=\mathrm{f}(|x|)\),[2]
    2. \(y=\frac1{\mathrm{f}(x)}\).[3]
  2. Express \(\frac{9x+5}{3x+2}\) in the form \(a-\frac b{3x+2}\) where \(a\) and \(b\) are positive constants.
    Hence, describe a sequence of transformations which transform the graph of \(y=\frac{9x+5}{3x+2}\) to the graph of \(y=\frac1x\).[5]

Solution:

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Answer:(a)(i) Asymptotes \(x=\pm4,y=0\); intercepts \((\pm2,0),(0,3)\); maximum \((0,3)\) (ii) Asymptotes \(x=2,y=\frac13\); intercept \((0,\frac13)\); minimum \((-5,\frac16)\); hole \((4,0)\) (b) \(a=3,b=1\); down 3, reflect in x-axis, right \(\frac23\), vertical stretch factor 3

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