Use the guidelines of this section to make a complete graph of f.
f(x) = x + 2 cos x on [-2π,2π)

Verified step by step guidance

1. Identify the function to be graphed: f(x) = x + 2 cos(x). This function is a combination of a linear term and a cosine term, which will affect its overall shape.
2. Determine the key features of the function, such as its periodicity due to the cosine component. The cosine function has a period of 2π, which will influence the behavior of f(x) over the interval [-2π, 2π).
3. Calculate the critical points by finding the derivative f'(x) = 1 - 2 sin(x) and setting it to zero to locate where the function has local maxima and minima.
4. Evaluate the function at key points within the interval, including endpoints and critical points, to understand the function's behavior. Consider points like -2π, -π, 0, π, and 2π.
5. Sketch the graph by plotting the calculated points and connecting them smoothly, taking into account the linear growth of x and the oscillating nature of the cosine function.