Combinations of Transformations (HSC SSCE Mathematics Advanced): Flashcards

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Combinations of Transformations
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Definition of commuting transformations

Transformations producing same result regardless of order applied

Two translations commute?

Yes, order doesn't matter

Two dilations commute?

Yes, order doesn't matter

Cross-direction transformations commute?

Yes (e.g., horizontal dilation + vertical translation)

Same-direction translation & dilation commute?

No, order matters and produces different results

Universal formula for transformations

y=kf(a(x+b))+cy = kf(a(x + b)) + c

Reflection in axes as dilation factor

−1-1

When does order of transformations matter?

When both act in same direction (both horizontal or vertical)

Horizontal translation + horizontal dilation commute?

No, order matters

Vertical translation + vertical dilation commute?

No, order matters

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