What is the general equation of a cosine function with an amplitude of 3 , a period of 4 pi , and a horizontal shift of negative pi ?

A cosine function has the form y = A cos(B(x − h)), where its amplitude is |A| and its period is 2π/|B|. An amplitude of 3 gives A = 3, and a period of 4π gives |B| = 2π/(4π) = 0.5. A horizontal shift of −π means h = −π, so the expression inside the cosine is x + π. Thus the function is y = 3 cos(0.5(x + π)), choice B.

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