Write a cosine function that has a midline of y=4 an amplitude of 2, a period of 4pi , and a horizontal shift of 2pi to the left. Answer Attemptiout of 2 f(x)=

## Step 1The general form of a cosine function is given by:### \(f(x) = A \cos(B(x - C)) + D\)where:- is the amplitude of the function,- is the frequency of the function,- is the horizontal shift of the function, and- is the midline of the function.## Step 2In this problem, we are given that the amplitude , the midline , the period , and the horizontal shift .## Step 3The frequency is related to the period by the formula:### Substituting the given period into the formula, we get:### ## Step 4Substituting the values of , , , and into the general form of the cosine function, we get:### \(f(x) = 2 \cos\left(\frac{1}{2}(x + 2\pi)\right) + 4\)