AQA · Mathematics · 8300
GCSE Maths: Transformations of trigonometric graphs
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Transformations of trigonometric graphs (Corbettmaths Video 324), 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 right if a is negative).
If point P(4, 1) is on y = f(x), what are the coordinates after transforming 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) is on y = f(x), what are the coordinates after transforming to y = f(x) + 4?
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(4, 5). The x-coordinate stays the same; 4 is added to the y-coordinate.
If point P(4, 1) is on y = f(x), what are the coordinates after transforming to y = f(−x)?
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(−4, 1). The x-coordinate is negated; the y-coordinate stays the same.
If point P(4, 1) is on y = f(x), what are the coordinates after transforming to y = f(x + 5)?
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(−1, 1). The graph shifts 5 units left, so subtract 5 from the x-coordinate; the y-coordinate stays the same.
If a curve y = f(x) has minimum point (5, 2), what is the minimum point of y = f(x − 2)?
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(7, 2). The graph shifts 2 units right, so add 2 to the x-coordinate; the y-coordinate stays the same.
The transformation from y = sin(x) to y = sin(x − 30°) is a horizontal translation ?.
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30° to the right
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