Function Translations — The Shifter
y = f(x) + a, y = f(x + a) for quadratic, sine, cosine
⚓ Phase 1: Vertical Shifts Only
Start simple. The transformation y = f(x) + a adds height AFTER the function calculates.
The "Outside" Rule: When the number is OUTSIDE the bracket, it happens AFTER f(x) computes.
Think of it as: calculate y = x² first, THEN add a to the result. Every y-coordinate gets shifted by +a.
Mark Scheme Tip: Always state the vector. Examiners award marks for writing the translation vector in column form.
PROBLEM: The curve y = x² is translated so that its minimum point is at (3, 5). Write down the equation of the new curve.
Click each step to reveal the working:
EXAMINER TRAP VAULT — Function Translations
❌ TRAP 1: Writing f(x + 3) for a shift RIGHT by 3. ✓ FIX: Right 3 means f(x − 3). Inside = Opposite!
❌ TRAP 2: Confusing y = f(x) + a with y = f(x + a). ✓ FIX: Outside (+a) = vertical. Inside (+a) = horizontal (opposite direction).
❌ TRAP 3: Forgetting to state the translation vector. ✓ FIX: Always write the column vector — examiners award a mark for it.
📊 Frequency: Very Common · 📉 Mark Impact: 2-3 marks per question
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