AQA · Mathematics · 8300
GCSE Maths: Transformations of graphs
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Transformations of graphs (Corbettmaths Video 323), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What transformation does y = −f(x) apply to the graph of y = f(x)?
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Reflection in the x-axis.
What transformation does y = f(x) + k apply to the graph of y = f(x)?
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Vertical translation (shift) by k units upward (or downward if k is negative).
What transformation does y = f(−x) apply to the graph of y = f(x)?
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Reflection in the y-axis.
What transformation does y = f(x + a) apply to the graph of y = f(x)?
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Horizontal translation (shift) by a units to the left (or to the right if a is negative).
If point P(4, 1) lies on y = f(x), what are the coordinates of P after the transformation to y = −f(x)?
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(4, −1). The x-coordinate stays the same; the y-coordinate is negated.
If point P(4, 1) lies on y = f(x), what are the coordinates of P after the transformation to y = f(x + 5)?
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(−1, 1). The graph shifts 5 units left, so x-coordinate becomes 4 − 5 = −1; y-coordinate stays the same.
If the minimum point of y = f(x) is at (5, 2), what is the minimum point of y = f(x) − 4?
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(5, −2). Vertical translation down by 4 units affects only the y-coordinate.
If the minimum point of y = f(x) is at (5, 2), what is the minimum point of y = f(x − 2)?
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(7, 2). Horizontal translation right by 2 units affects only the x-coordinate.
For the transformation y = f(x + 1) − 2, how are the coordinates of the minimum point transformed?
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The x-coordinate shifts left by 1, and the y-coordinate shifts down by 2.
What transformation maps y = sin(x) onto y = sin(x − 30°)?
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Horizontal translation (shift) 30° to the right.
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