The problem presents an exponential transformation of the parent function $f(x) = 2^x$, and you're tasked with identifying the graph of the transformed function $g(x) = 2^x + 3$.

This transformation shifts the parent function vertically by 3 units upward. Therefore, the correct graph should show the same general shape as $2^x$, but with its horizontal asymptote moved from $y = 0$ to $y = 3$.

Looking at the provided options:

• Option A: This graph starts from below the x-axis and increases, which is not consistent with the vertical shift upward.
• Option B: This graph starts from below the x-axis, increasing more sharply, which is inconsistent.
• Option C: This graph shows an exponential increase with the correct behavior above the x-axis, but it doesn't shift up by exactly 3 units.
• Option D: This graph is the correct one. It shows the exponential curve shifted upwards by 3 units, as expected for the function $g(x) = 2^x + 3$.

Thus, the correct answer is D.

Would you like a detailed explanation or have any questions about the transformation? Here are some related questions to explore further:

1. How does adding a constant to an exponential function affect its graph?
2. How would the graph change if we had $g(x) = 2^x - 3$?
3. What is the role of the horizontal asymptote in exponential functions?
4. How would the graph change if the transformation were a horizontal shift instead of a vertical one?
5. What other examples of exponential transformations can you think of?

Tip: Remember that for exponential functions, vertical shifts are added or subtracted outside the base, while horizontal shifts affect the exponent.