Sketching Rational Functions with Horizontal Asymptote Only

Sketch rational functions where the degree of the numerator is less than or equal to the degree of the denominator, so only horizontal and vertical asymptotes are present.

2 questions · Standard +0.3

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OCR MEI FP1 2009 June Q7
12 marks Standard +0.3
7 A curve has equation \(y = \frac { ( x + 2 ) ( 3 x - 5 ) } { ( 2 x + 1 ) ( x - 1 ) }\).
  1. Write down the coordinates of the points where the curve crosses the axes.
  2. Write down the equations of the three asymptotes.
  3. Determine whether the curve approaches the horizontal asymptote from above or below for
    (A) large positive values of \(x\),
    (B) large negative values of \(x\).
  4. Sketch the curve.
OCR MEI FP1 2011 June Q7
12 marks Standard +0.3
7 A curve has equation \(y = \frac { ( x + 9 ) ( 3 x - 8 ) } { x ^ { 2 } - 4 }\).
  1. Write down the coordinates of the points where the curve crosses the axes.
  2. Write down the equations of the three asymptotes.
  3. Determine whether the curve approaches the horizontal asymptote from above or below for
    (A) large positive values of \(x\),
    (B) large negative values of \(x\).
  4. Sketch the curve.