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Gresty Academy Paper 2 · Q13

Paper 2Logic & proofFunctions & graphs

If the graph of y=f(x)y=f(x) translated 33 right and then reflected in the y-axis is identical to the graph of y=f(x)y=f(x) reflected in the y-axis and then translated 33 right, which of the following must be true for all xx?

Af(x)+f(x+6)=2f(x+3)f(x)+f(x+6)=2f(x+3)
Bf(x)−f(x+6)=2f(x+3)f(x)-f(x+6)=2f(x+3)
Cf(x)+f(x+12)=2f(x+6)f(x)+f(x+12)=2f(x+6)
Df(x)−f(x+12)=2f(x+6)f(x)-f(x+12)=2f(x+6)
Ef(x)+f(x+3)=2f(x+6)f(x)+f(x+3)=2f(x+6)

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