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 4 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and 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)!
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?
Describe fully each of the following transformations of y = f(x): (a) y = 3f(x) (b) y = f(2x) (c) y = f(x) - 5
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)