Translations and reflections of functions
Higher-only on Edexcel 1MA1, examined on Paper 1H or 2H. Pupils transform a graph y = f(x) by adding/subtracting inside or outside the function.
Translation rules
- y = f(x) + a: translates UP by a (or down if a < 0). Vector (0, a).
- y = f(x + a): translates LEFT by a (or right if a < 0). Vector (−a, 0). Note the sign flip.
- y = f(x − a): translates RIGHT by a. Vector (a, 0).
A handy mnemonic: changes inside the bracket affect x and act in the opposite direction. Changes outside affect y and act in the same direction.
Reflection rules
- y = −f(x): reflection in the x-axis (flip up/down).
- y = f(−x): reflection in the y-axis (flip left/right).
Combining transformations
y = −f(x − 2) + 3: take f(x), reflect in x-axis, translate right by 2 and up by 3. Order: do the reflection / scaling first, then the translations.
Effect on key points
If (a, b) is on y = f(x):
- It maps to (a, b + 3) on y = f(x) + 3.
- It maps to (a − 5, b) on y = f(x + 5).
- It maps to (a, −b) on y = −f(x).
- It maps to (−a, b) on y = f(−x).
Common Edexcel mark-scheme phrasing
- B1 for correct shape (preserved through translations and reflections).
- B1 for the correct translation vector applied.
- B1 for at least one labelled key point on the new graph (often a turning point or intercept).
⚠Common mistakes— Common errors
- Translating the wrong direction for "inside the bracket" changes (f(x − 2) goes RIGHT, not left).
- Reflecting in the wrong axis: −f(x) is x-axis reflection (flip vertically).
- Combining transformations in the wrong order.
- Forgetting to translate ALL key points, not just the turning point.
AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves