The resulting equation for the graph is f(x) = 2 cos(x/2) + 1.
The graph appears to be a cosine function with amplitude 2, midline y = 1, and period 4π. Here's how we can find the equation in the form f(x) = A cos(Bx + C) + D:
**1. Amplitude and midline:**
The amplitude is half the distance between the maximum and minimum values, which is 2 in this case. So, A = 2.
The midline is the average of the maximum and minimum values, which is 1 in this case. So, D = 1.
**2. Period and phase shift:**
The period is the horizontal distance between two consecutive peaks (or troughs). In this case, the distance between two peaks is 4π. Therefore, 2π/B = 4π, and solving for B gives us B = 1/2.
The phase shift is the horizontal distance between the midline and the nearest peak (or trough) to the left. In this case, there is no phase shift, as the peak touches the midline. Therefore, C = 0.
**3. Putting it all together:**
Now we can plug the values of A, B, C, and D into the equation:
f(x) = A cos(Bx + C) + D = 2 cos((1/2)x + 0) + 1 = 2 cos(x/2) + 1
Therefore, the equation for the cosine graph is f(x) = 2 cos(x/2) + 1.
The question probable is given in the attachment.