Transformations of Graphs

Understanding how to transform the graph of y = f(x) is a fundamental skill at A-Level. The Edexcel 9MA0 specification requires you to apply translations, stretches and reflections to known graphs, and to combine transformations. You must also know how transformations affect the equation of the curve.

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Translations

Vertical Translation: y = f(x) + a

This translates the graph a units upward (if a > 0) or |a| units downward (if a < 0).

Every point (x, y) on y = f(x) maps to (x, y + a).

The translation vector is (0, a).

Example: y = x² + 3 is the graph of y = x² translated 3 units upward.

Horizontal Translation: y = f(x − a)

This translates the graph a units to the right (if a > 0) or |a| units to the left (if a < 0).

Every point (x, y) on y = f(x) maps to (x + a, y).

The translation vector is (a, 0).

Example: y = (x − 2)² is the graph of y = x² translated 2 units to the right.