Questions — AQA FP1 (176 questions)

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AQA FP1 2006 June Q9
9 A curve \(C\) has equation $$y = \frac { ( x + 1 ) ( x - 3 ) } { x ( x - 2 ) }$$
    1. Write down the coordinates of the points where \(C\) intersects the \(x\)-axis. (2 marks)
    2. Write down the equations of all the asymptotes of \(C\).
    1. Show that, if the line \(y = k\) intersects \(C\), then $$( k - 1 ) ( k - 4 ) \geqslant 0$$
    2. Given that there is only one stationary point on \(C\), find the coordinates of this stationary point.
      (No credit will be given for solutions based on differentiation.)
  3. Sketch the curve \(C\).