Find the function that is finally graphed after the following transformations are applied to the graph of y=√x in the order listed.

1) Reflect about the x-axis
2) Shift up 7 units
3) Shift right 4 units

To find the function that is finally graphed after the given transformations are applied to the graph of y = √x, we need to apply the transformations in the order listed.

1) Reflect about the x-axis: This transformation changes the sign of the y-coordinate. So, the reflected function will be y = -√x.

2) Shift up 7 units: This transformation moves the entire graph upward by 7 units. To achieve this, we can add 7 to the y-coordinate. Therefore, the new function becomes y = -√x + 7.

3) Shift right 4 units: This transformation moves the entire graph to the right by 4 units. To achieve this, we can subtract 4 from the x-coordinate. Therefore, the final function is y = -√(x - 4) + 7.

So, the function that is finally graphed after the given transformations are applied in the order listed is y = -√(x - 4) + 7.