GraphsKey Facts

Transformation Rules (THE Table!)

Part of Graph TransformationsGCSE Mathematics

This key facts covers Transformation Rules (THE Table!) within Graph Transformations for GCSE Mathematics. Revise Graph Transformations in Graphs for GCSE Mathematics with 14 exam-style questions and 1 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 2 of 3 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 2 of 3

Practice

14 questions

Recall

1 flashcards

Transformation Rules (THE Table!)

Transformation Effect Example from y = f(x)
f(x) + a Translate UP by a y = x² + 3 moves up 3
f(x) − a Translate DOWN by a y = x² − 2 moves down 2
f(x + a) Translate LEFT by a y = (x + 3)² moves left 3
f(x − a) Translate RIGHT by a y = (x − 2)² moves right 2
af(x) Stretch vertically by factor a y = 3x² stretches ×3 vertically
f(ax) Squash horizontally by factor a y = (2x)² squashes ×2 horizontally
−f(x) Reflect in x-axis y = −x² flips upside down
f(−x) Reflect in y-axis y = (−x)² flips left-right

Memory trick: Inside brackets = opposite direction (+ goes left, − goes right)!

Keep building this topic

Read this section alongside the surrounding pages in Graph Transformations. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Graph Transformations

The graph of y = f(x) is transformed to y = f(x) + 3. Which of the following describes this transformation?

  • A. Translation 3 units to the right
  • B. Translation 3 units upwards
  • C. Stretch by scale factor 3 parallel to the y-axis
  • D. Translation 3 units to the left
1 markfoundation

Describe fully each of the following transformations of y = f(x): (a) y = 3f(x) (b) y = f(2x) (c) y = f(x) - 5

3 marksstandard

Quick Recall Flashcards

f(x + a) vs f(x) + a
f(x + a) = LEFT by a (inside, opposite). f(x) + a = UP by a (outside, same direction)

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