Transforming Graphs – Questions Answered | Pearson Edexcel International GCSE Maths

These examples look at transformations of the graph y = f(x). The original curve has a minimum point at (2, −1). By examining how the function changes, we can determine how the coordinates of this minimum point are transformed.

Original Minimum Point

The curve y = f(x) has a minimum point at:

(2, −1)

Question (a)(i) – y = f(x + 2)

Find the coordinates of the minimum point after the transformation y = f(x + 2).

Working

y = f(x + 2)

* Translation
(−2, 0)

Answer: (0, −1)
Answer: (0, −1)

Question (a)(ii) – y = 3f(x)

Find the coordinates of the minimum point after the transformation y = 3f(x).

Working

y = 3f(x)

* Multiply y-coordinate by 3.

Answer: (2, −3)
Answer: (2, −3)

Question (a)(iii) – y = f(2x)

Find the coordinates of the minimum point after the transformation y = f(2x).

Working

y = f(2x)

* Multiply the x-coordinate by 1/2.

Answer: (1, −1)
Answer: (1, −1)

Understanding the Transformations

Transformations outside the function affect the y-coordinate, while transformations inside the function affect the x-coordinate.

For:

y = 3f(x)

every y-coordinate is multiplied by 3. Therefore:

(2, −1) → (2, −3)

For:

y = f(2x)

every x-coordinate is multiplied by 1/2. Therefore:

(2, −1) → (1, −1)

Question (b) – Reflection in the y-axis

The curve y = f(x) is reflected in the y-axis. Find the equation of the transformed curve.

Working

The curve y = f(x) is reflected in the y-axis.

y = f(−x)
Answer: y = f(−x)

Transformation Summary

y = f(x + 2)
Translation 2 units to the left:
(2, −1) → (0, −1)

y = 3f(x)
Multiply the y-coordinate by 3:
(2, −1) → (2, −3)

y = f(2x)
Multiply the x-coordinate by 1/2:
(2, −1) → (1, −1)

Reflection in the y-axis:
y = f(−x)

Source: Question adapted from Harry Smith, Revise Pearson Edexcel International GCSE (9–1) Mathematics A – Higher Tier Revision Guide, Pearson.

Solutions and workings: Tiago Hands.

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