https://file.aiquickdraw.com/mathbot/file/1727209073844bpziu937.jpg

The given function in the image is \( f(x) = \sqrt{x} \). According to the problem, the function is to be translated 2 units to the left and 1 unit down.

### Step-by-step solution:

1. **Horizontal Translation (Left by 2 units)**:
   To move a function \( f(x) \) 2 units to the left, we replace \( x \) with \( x + 2 \). Therefore, the new function becomes:
   \[
   f(x) = \sqrt{x + 2}
   \]

2. **Vertical Translation (Down by 1 unit)**:
   To move a function down by 1 unit, we subtract 1 from the entire function. So, the new function is:
   \[
   f(x) = \sqrt{x + 2} - 1
   \]

### Final Transformed Function:
Thus, the final form of the function after the translation is:
\[
f(x) = \sqrt{x + 2} - 1
\]

Would you like further details or have any questions?

### Related Questions:
1. How would the function change if it were translated 3 units to the right instead of left?
2. What happens to the domain of the function \( f(x) = \sqrt{x} \) after translation?
3. Can this transformation be represented graphically? How does the graph look after translation?
4. How do you reflect a square root function across the y-axis?
5. How do you find the inverse of \( f(x) = \sqrt{x} \)?

### Tip:
When translating functions, always adjust the variable inside the function for horizontal shifts and adjust the entire function output for vertical shifts.

Fungsi f(x) = √x ditranslasikan 2 satuan ke kiri dan 1 satuan ke bawah. Bentuk fungsi hasil translasi adalah?

Learn how to translate the function f(x) = √x by 2 units left and 1 unit down. This step-by-step guide covers key algebraic concepts, including horizontal and vertical translations. Suitable for students in Grades 9-12.

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