1. **Problem Statement:** We are given a cosine graph that has been vertically shifted. The general form of the function is $$y = \cos(x) + C$$ where $$C$$ is the vertical shift. 2. **Understanding the cosine function:** The basic cosine function $$y = \cos(x)$$ oscillates between -1 and 1 with a midline at $$y=0$$. 3. **Vertical shift:** If the graph is shifted vertically by $$C$$ units, the midline moves from $$y=0$$ to $$y=C$$. 4. **Analyzing the graph:** From the description, the wave ranges approximately from -6 to 5. 5. **Calculate the vertical shift:** The amplitude of cosine is 1, so the range of $$y=\cos(x)$$ is $$[-1,1]$$. If the graph is shifted by $$C$$, the new range is $$[C-1, C+1]$$. Given the range is approximately $$[-6,5]$$, we set: $$C - 1 = -6$$ and $$C + 1 = 5$$ 6. **Solve for $$C$$:** From $$C - 1 = -6$$, we get $$C = -5$$. From $$C + 1 = 5$$, we get $$C = 4$$. These two values contradict, so we re-examine the range. 7. **Re-examining the range:** The range from -6 to 5 is asymmetric, which is unusual for a cosine function with a vertical shift only. Assuming the graph's midline is at the average of the max and min: $$C = \frac{-6 + 5}{2} = \frac{-1}{2} = -0.5$$ 8. **Check amplitude:** Amplitude $$A = \frac{5 - (-6)}{2} = \frac{11}{2} = 5.5$$ Since the amplitude is not 1, the function is actually: $$y = 5.5 \cos(x) - 0.5$$ 9. **Final equation:** The vertical shift is $$-0.5$$. **Answer:** $$y = 5.5 \cos(x) - 0.5$$