2025 CJC Promo Q9

2025 CJC Promo Q9

Junior College 1
9 marks

  1. The curve \(C\) has equation \(y=\frac{x^2+4x-5}{x-5},\quad x\in\mathbb{R},\quad x\ne 5.\)

    1. Sketch \(C\), stating the equations of the asymptotes, axial intercepts and the coordinates of the turning points, if any.[4]
    2. Hence, by sketching another suitable graph on the same axes as in part (a)(i), solve the inequality \(\frac{x^2+4x-5}{2x-10}\ge \ln(x+5)\).[3]

  2. Describe a pair of transformations which would transform curve \(C\) onto the graph of \(y=\frac{4x^2+8x-5}{2x-5}-2.\)

    [2]

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Answer:(a)(ii) \(-5<x\leq-3.52\) or \(x>5\) (b) horizontal scale factor \(\dfrac12\), then translate down \(2\)

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