The given problem involves the function $g(x) = \sqrt{x}$, and the transformation involves shifting it 4 units to the left. To represent this transformation mathematically, we adjust the input of the square root function as follows:

The transformation:

• Shifting left 4 units corresponds to $g(x) \to g(x+4)$.

Thus, the transformed equation becomes: $f(x) = \sqrt{x+4}.$

Steps to identify the correct graph:

1. The graph of $\sqrt{x}$ starts at the origin $(0, 0)$ and extends to the right, with a gradual increase in the $y$-values.
2. Shifting it 4 units left means the starting point of the graph moves from $(0, 0)$ to $(-4, 0)$.
3. Look for a graph where the curve begins at $(-4, 0)$ and follows the square root function's increasing pattern.

Answer: The correct graph is option B.

Would you like further clarification on graph transformations or additional details? Here are some related questions to consider:

1. What happens if you shift $\sqrt{x}$ to the right instead of left?
2. How do transformations like reflections or vertical shifts affect square root graphs?
3. Can you explain how to determine the domain and range of $\sqrt{x+4}$?
4. What is the significance of horizontal shifts in general functions?
5. How does the graph of $\sqrt{x}$ compare to other radical functions like $\sqrt[3]{x}$?

Tip: Always remember that shifting a graph horizontally changes the function's input, while vertical shifts affect the output directly.