Transformations of Functions (AQA A-Level Mathematics): Quizzes

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Stretches
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Which notation represents a vertical stretch of f(x)f(x) by a constant factor aa?

y=af(x)y = af(x)

For y=af(x)y = af(x), when is this a vertical stretch rather than a compression?

When a>1|a| > 1

What happens to points on the graph during a vertical stretch with a>1|a| > 1?

Move further from x-axis

Which notation represents a horizontal stretch of f(x)f(x) by a factor bb?

y=f(x/b)y = f(x/b)

For y=f(x/b)y = f(x/b), when is this a horizontal stretch rather than a compression?

When b>1|b| > 1

If f(x)=x2f(x) = x^2, what transformation is y=2x2y = 2x^2?

Vertical stretch by factor 2

What visual effect does a horizontal stretch with b>1|b| > 1 have on the graph?

Graph becomes wider

For y=3sin(x)y = 3\sin(x), what happens to the amplitude of the sine wave?

Increases from 1 to 3

For y=sin(x/2)y = \sin(x/2), what is the new period of the sine wave?

4π4\pi

What do horizontal stretches affect in a function?

Input (x-values)

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