Translating Functions in MYP Extended Maths
Learn how translations shift graphs in MYP Extended Maths Year 5. Master f(x)+a and f(x+a) with direction rules, worked examples and common mistakes to avoid.
What Is a Translation?
A translation moves a graph horizontally or vertically without changing its shape, size, or orientation. This is the first of four transformation types you will study at Extended level. Understanding translations precisely is essential before tackling reflections, stretches, and combined transformations.
Vertical Translations: f(x) + a
Adding a constant outside the function shifts the graph vertically. If y = f(x) + a:
- When a > 0, the graph shifts up by a units.
- When a < 0, the graph shifts down by |a| units.
Every point (x, y) on the original graph becomes (x, y + a). The shape is identical; only the position changes. Check this by tracing a specific point — for example, if the minimum of f(x) is at (2, 1), the minimum of f(x) + 3 is at (2, 4).
Horizontal Translations: f(x + a)
Adding a constant inside the function — replacing x with (x + a) — shifts the graph horizontally, and the direction is counterintuitive:
- f(x + a) shifts the graph left by a units (when a > 0).
- f(x − a) shifts the graph right by a units (when a > 0).
This confuses many students. The reason: f(x + 2) = 0 when x = −2, so the root moves left. Always reason from a specific point to confirm the direction.
Applying Translations to Different Functions
Practise translating linear, quadratic, and other standard curves. For a parabola y = x², the graph of y = (x − 3)² + 2 has its vertex at (3, 2) — shifted right 3 and up 2. Recognising translations in the equation is an important Criterion A and C skill.
Common Mistakes
- Confusing the direction of horizontal translations — f(x + 3) moves left, not right.
- Applying a vertical translation to the x-coordinate instead of the y-coordinate.
- Not updating all key features (vertex, intercepts, asymptotes) when translating.