To write the function whose graph is the same as $y = \sqrt{x}$, but shifted up 4 units, you add 4 to the original function. This shifts the graph vertically.

The function would be:

$y = \sqrt{x} + 4$

Explanation:

• The original function is $y = \sqrt{x}$, which is the graph of the square root of $x$.
• To shift a graph vertically, you add or subtract a constant. Adding a constant shifts the graph up. In this case, adding 4 shifts the graph up by 4 units.

Would you like further details on graph transformations or have any other questions?

Here are some related questions:

1. How do you shift a graph down by a certain number of units?
2. How would you shift $y = \sqrt{x}$ to the right by 3 units?
3. What happens to the graph of $y = \sqrt{x}$ when you multiply it by a negative number?
4. How do vertical stretches affect the graph of $y = \sqrt{x}$?
5. Can you explain how to shift a function both horizontally and vertically at the same time?

Tip: To shift a graph horizontally, you modify the variable inside the function, but to shift vertically, you modify the function itself by adding or subtracting constants.