The question is asking for a translation of the function $f(x) = \sqrt{x}$.

A translation involves shifting the graph of the function either horizontally, vertically, or both. The problem specifies the following translation:

• 2 units down: This affects the vertical position of the graph and is represented by subtracting 2 from the function.
• 1 unit to the left: A leftward horizontal shift is represented by adding 1 to the $x$-value.

To apply this translation, the transformed function would be:

$f(x) = \sqrt{x} \quad \text{becomes} \quad f(x) = \sqrt{x + 1} - 2$

Thus, the translated function is:

$f(x) = \sqrt{x + 1} - 2$

Would you like further details or have any questions?

Here are five follow-up questions related to this concept:

1. How would the function change if the shift were 3 units to the right and 4 units up?
2. What would be the effect of reflecting the function $f(x) = \sqrt{x}$ across the x-axis?
3. How does a horizontal stretch or compression affect the function $f(x)$?
4. What is the domain of the translated function $f(x) = \sqrt{x + 1} - 2$?
5. How would you graph the function after the translation?

Tip: Horizontal shifts affect the $x$-values inside the function, while vertical shifts affect the function’s overall output directly.