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WMA11/01 Jun 2022, Question 4: Transformations with Asymptotes

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

From the given sketch of y = f(x) with minimum P(−1, 0), maximum Q(3/2, 2) and asymptote y = 1, sketch two transformed curves on separate diagrams, stating new max/min coordinates and asymptote.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (i) · 3 marks

Sketch y = f(x) − 2, giving the coordinates of the new maximum and minimum and the equation of the asymptote.

  1. 1Subtract 2 from every y-coordinate
  2. 2P(−1, 0) → (−1, −2) and Q(3/2, 2) → (3/2, 0)
  3. 3Asymptote y = 1 → y = −1

AnswerSketch: the same curve moved down 2 — minimum (−1, −2), maximum (3/2, 0) touching the x-axis, asymptote y = −1.

Part (ii) · 3 marks

Sketch y = f(−x), giving the coordinates of the new maximum and minimum and the equation of the asymptote.

  1. 1Reflect in the y-axis: change the sign of every x-coordinate
  2. 2Q(3/2, 2) → (−3/2, 2) and P(−1, 0) → (1, 0)
  3. 3Asymptote stays y = 1

AnswerSketch: the curve reflected in the y-axis — maximum (−3/2, 2), minimum (1, 0) touching the x-axis, asymptote y = 1.

Stuck on a step? Read the free lesson: Transformations with Asymptotes

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