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 $y$).