https://file.aiquickdraw.com/mathbot/file/17284479628308647cu3b.jpg

The image shows the graph of \( y = \sqrt{x} \), and the instruction asks to translate it into the graph of \( y = \sqrt{x - 4} + 3 \).

### Steps for Translation:
- **Horizontal Translation**: The term \( x - 4 \) inside the square root function translates the graph **4 units to the right**. This is because subtracting a number from \( x \) shifts the graph horizontally.
  
- **Vertical Translation**: The term \( + 3 \) outside the square root function translates the graph **3 units up**. Adding a constant shifts the graph vertically.

### Result:
To obtain the graph of \( y = \sqrt{x - 4} + 3 \), you would take the original graph of \( y = \sqrt{x} \), move it **4 units to the right** and **3 units up**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do other transformations like reflections affect square root graphs?
2. What is the domain and range of \( y = \sqrt{x - 4} + 3 \)?
3. How would the graph change if it were \( y = -\sqrt{x - 4} + 3 \)?
4. What are the key points (like intercepts) on the graph of \( y = \sqrt{x} \) after translation?
5. How would this graph relate to a cubic or quadratic graph?

**Tip**: When translating graphs, remember that horizontal shifts are determined by changes inside the function (affecting \( x \)) while vertical shifts are outside the function (affecting \( y \)).

Below is the graph of y = √x. Translate it to make it the graph of y = √(x - 4) + 3.

Understand how to translate the graph of y = √x into y = √(x - 4) + 3. This problem involves horizontal and vertical shifts, with a step-by-step breakdown of how to move the graph 4 units right and 3 units up. Suitable for students in Grades 9-12.

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