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4MA1/2HR Jun 2022, Question 22: Transformations of Graphs

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks

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The question, in short

Given A(−3, 2) on y = f(x), find image coordinates under two transformations, then use a sketch of y = g(x) with B(p, q) to find the image of B under a third transformation.

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

Part (ai) · 1 mark

State where A(−3, 2) moves when the graph is shifted down by 3.

  1. 1Original point A: (−3, 2)
  2. 2Apply transformation: y = f(x) − 3
  3. 3y-coordinate becomes 2 − 3 = −1
  4. 4x-coordinate remains −3
  5. 5Image: (−3, −1)

Answer(−3, −1)

Part (aii) · 1 mark

State where A(−3, 2) moves when x is replaced by x/2.

  1. 1Original point A: (−3, 2)
  2. 2Apply transformation: y = f(x/2)
  3. 3x is replaced by x/2, so to get same y, x must be doubled
  4. 4New x-coordinate: −3 × 2 = −6
  5. 5y-coordinate remains 2
  6. 6Image: (−6, 2)

Answer(−6, 2)

Part (b) · 2 marks

Using B(p, q) on y = g(x), give the coordinates of its image under y = −g(x − c).

  1. 1Original point B: (p, q)
  2. 2Apply transformation: y = −g(x − c)
  3. 3x is replaced by x − c → shift right by c → new x: p + c
  4. 4Negative sign reflects in x-axis → new y: −q
  5. 5Image: (p + c, −q)

Answer(p + c, −q)

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