# Graph Transformations - Proofs

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Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths. Transformations of Graphs Proof (Translations, Reflections, Stretches)

Transformations of Graphs (translations) Proof
Why y=f(x ± a) translates a graph left and right and y=f(x) ± a translates a graph up and down depending on the value of ‘a’.

Transformations of Graphs (Reflections) Proof
Why y= -f(x) reflects a graph in the x-axis and why y=f(-x) reflects a graph in the y-axis?

Transformations of Graphs (stretches 1) Proof
Why y = af(x) stretches a graph y=f(x) by a factor of ‘a’ parallel to the y-axis?

Transformations of Graphs (stretches 2) Proof
Why y=f(ax) stretches the graph by a factor of ‘1/a’ parallel to the x-axis?

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