Transformations of Graphs Flashcards

GCSE Mathematics (Edexcel) 1MA1

Translation of a graph by vector (a, b)

Adds 'a' to the x-coordinates and 'b' to the y-coordinates of all points on the graph.

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Translation of a graph by vector (a, b)

Adds 'a' to the x-coordinates and 'b' to the y-coordinates of all points on the graph.

Effect of y = f(x) + k

Shifts the graph of y = f(x) vertically by k units. Positive k moves it up, negative k moves it down.

Effect of y = f(x + k)

Shifts the graph of y = f(x) horizontally by k units. Positive k moves it left, negative k moves it right.

Reflection in the x-axis

The graph of y = f(x) becomes y = -f(x).

Reflection in the y-axis

The graph of y = f(x) becomes y = f(-x).

Vertical stretch by scale factor a

The graph of y = f(x) becomes y = a × f(x). Stretches the graph away from the x-axis if a > 1, compresses it if 0 < a < 1.

Horizontal stretch by scale factor 1/a

The graph of y = f(x) becomes y = f(ax). Stretches the graph away from the y-axis if 0 < a < 1, compresses it if a > 1.

Effect of y = |f(x)|

Reflects any part of the graph of y = f(x) below the x-axis above the x-axis.

Effect of y = f(|x|)

Replaces the left-hand side of the graph of y = f(x) with a reflection of the right-hand side in the y-axis.

Combination of transformations

Apply transformations in the correct order, starting with stretches and reflections, followed by translations.

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