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WMA11/01 Jun 2024, Question 3: Transformations of Graphs

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

The question, in short

Sketch transformations of the curve y = f(x) through (−1, 0), (0, 2) and touching the x-axis at (3, 0), showing axis intercept coordinates.

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

Part (a) · 3 marks

Sketch y = f(x + 3), giving coordinates of all points where the curve meets the axes.

  1. 1f(x + 3) is a translation of 3 units in the negative x-direction
  2. 2(−1, 0) moves to (−4, 0)
  3. 3(3, 0) moves to (0, 0): the curve touches the x-axis at the origin (minimum)
  4. 4Shape unchanged: cross at (−4, 0), up to a maximum, down to touch at (0, 0), then up

AnswerSame shape moved 3 units left: crosses the x-axis at (−4, 0), maximum between x = −4 and x = 0, touches the x-axis at the origin (0, 0), which is a minimum, then rises

Part (b) · 3 marks

Sketch y = f(−3x), giving coordinates of all points where the curve meets the axes.

  1. 1f(−3x): reflect in the y-axis and stretch by scale factor 1/3 in the x-direction
  2. 2x-values: −1 → 1/3 and 3 → −1; y-values unchanged
  3. 3Touches the x-axis at (−1, 0) (minimum); crosses it at (1/3, 0)
  4. 4y-intercept stays at (0, 2); the maximum is now just left of the y-axis

AnswerReflection in the y-axis with x-values divided by 3: comes down from the top left to touch the x-axis at (−1, 0) (minimum), rises to a maximum to the left of the y-axis, passes through (0, 2), then falls to cross the x-axis at (1/3, 0) and continues down

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Also searched as: WMA11 June 2024 · WMA11/01 · wma11 jun24 · IAS Maths Pure Mathematics 1 June 2024 · question 3.
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