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What cosine function represents an amplitude of 2, a period of 2π, a horizontal shift of π, and a vertical shift of −1?

User Mushroom
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1 Answer

1 vote

Answer:


f(x)=2\cos(x-\pi)-1

Explanation:

The general cosine function is given by


f(x)=A\cos(Bx-C)+D

where
A=2 is the amplitude,


Period=(2\pi)/(B)


\Rightarrow 2\pi=(2\pi)/(B)


\Rightarrow B=1,


c=\pi is the horizontal shift and
D=-1 is a downward vertical shift.

If we substitute all these values into the formula we obtain;


f(x)=2\cos(x-\pi)-1

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