Translations (AQA A-Level Mathematics): Flashcards

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Translations
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Effect of f(xa)f(x - a) on graph of f(x)f(x)

Shifts right by aa units

Effect of f(x+a)f(x + a) on graph of f(x)f(x)

Shifts left by aa units

Effect of f(x)+bf(x) + b on graph of f(x)f(x)

Shifts up by bb units

Effect of f(x)bf(x) - b on graph of f(x)f(x)

Shifts down by bb units

What stays constant in horizontal translation?

yy-values stay same, xx-values change

What stays constant in vertical translation?

xx-values stay same, yy-values change

General form: translate aa right & bb up

y=f(xa)+by = f(x - a) + b

Translation vector (32)\begin{pmatrix} 3 \\ -2 \end{pmatrix} means

3 units right, 2 units down

Translation vector (23)\begin{pmatrix} -2 \\ 3 \end{pmatrix} means

2 units left, 3 units up

x+23|x + 2| - 3 transformation from x|x|

2 units left, 3 units down

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