Combinations of Transformations (HSC SSCE Mathematics Advanced): Quizzes

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Combinations of Transformations
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What does it mean for two transformations to commute?

They produce same result in any order

Do two translations always commute?

Yes, order doesn't matter

Do two dilations always commute?

Yes, order doesn't affect the result

Does a horizontal dilation commute with a vertical translation?

Yes, cross-direction transforms commute

When do transformations NOT commute?

When both act in the same direction

Shifting y=x2y = x^2 right 3 and down 1 (any order) gives which equation?

y=(x−3)2−1y = (x-3)^2 - 1

Stretching x2+y2=1x^2 + y^2 = 1 horiz. by 3, vert. by 2 (any order) gives what?

x29+y24=1\frac{x^2}{9} + \frac{y^2}{4} = 1

Do horizontal translation and horizontal dilation commute?

No, same-direction transforms don't

Do vertical translation and vertical dilation commute?

No, both vertical so order matters

In y=kf(a(x+b))+cy = kf(a(x+b)) + c, what does kk represent?

Vertical stretch factor

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