Reflections (AQA A-Level Mathematics): Flashcards

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Reflections
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Formula for reflection in xx-axis

y=−f(x)y = -f(x)

Point mapping: xx-axis reflection

(x,y)(x, y) becomes (x,−y)(x, -y)

Formula for reflection in yy-axis

y=f(−x)y = f(-x)

Point mapping: yy-axis reflection

(x,y)(x, y) becomes (−x,y)(-x, y)

Formula for reflection in both axes

y=−f(−x)y = -f(-x)

Effect of reflecting in both axes

180° rotation around origin

f(x)=x2f(x) = x^2 reflected in xx-axis

y=−x2y = -x^2

f(x)=x3f(x) = x^3 reflected in yy-axis

y=−x3y = -x^3

Domain of −x\sqrt{-x} (yy-axis reflection)

x≤0x \leq 0

1x\frac{1}{x} reflected in both axes

1x\frac{1}{x} (returns to original)

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