The given question asks to find the function $g(x)$ that results from shifting the function $f(x) = 2^x$ one unit upward.

To solve this, note that a vertical shift of one unit upward for any function $f(x)$ results in a new function given by: $g(x) = f(x) + 1$ Since $f(x) = 2^x$, applying this transformation yields: $g(x) = 2^x + 1$

Therefore, the correct answer is $g(x) = 2^x + 1$, which corresponds to option A.

Let me know if you need further details, and feel free to ask more questions! Here are some related questions:

1. What is the effect of shifting a function horizontally?
2. How does multiplying a function by a constant affect its graph?
3. What happens when you reflect a function across the x-axis?
4. Can you describe the transformation when a function is shifted downward by 3 units?
5. How would the graph of $f(x) = 2^x$ change if the function were $f(x) = 2^{-x}$?

Tip: Remember that shifting a function upward or downward does not change its overall shape, only its vertical position.