Here is the graph of \( y = \cos(x) + 2 \), showing the oscillation between 1 and 3 with a vertical shift upward by 2 units.

Would you like more details about any part of the graph or its properties?

Here are 5 related questions for further exploration:
1. How would the graph change if the function was \( y = \cos(x) - 2 \)?
2. What happens to the graph if we multiply the function by a constant, e.g., \( y = 2\cos(x) + 2 \)?
3. How does the period of the graph change if the argument is modified to \( y = \cos(2x) + 2 \)?
4. Can you explain the phase shift in the cosine function, and how would it affect \( y = \cos(x - \pi/2) + 2 \)?
5. What is the significance of the amplitude and how can we adjust it in the equation?

**Tip**: When graphing transformations, always identify vertical shifts, amplitude changes, and period adjustments first for a clear understanding of how the graph is affected.

Explore the graph of y = cos(x) + 2, highlighting key transformations such as vertical shifts and amplitude changes. This solution covers the fundamental trigonometric concepts needed to understand how the graph oscillates between 1 and 3, with a vertical shift by 2 units. Suitable for high school students in Grades 9-12.

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