What cosine function represents an amplitude of 2, a period of 2π, a horizontal shift of π, and a vertical shift of −1? (multiple choice) !

The formula for a cosine graph is: f(x) = acosb(x - k) + h where a is the amplitude, b is the period factor, k is the phase shift and h is the horizontal shift. Knowing that the amplitude is 2, we can already rule out #1 and #2. If the period is 2π, b = 1 because the formula for period is . The horizontal shift is π, so we plug that in for k, and h = 1. Now, we plug everything in and you get:

f(x) = 2 cos (x - π) + 1

Option 3 is your answer.

Hope this helps!