Step 1 :The transformations applied to the function \(y=\sqrt{x}\) are shifting down by 9 units, reflecting about the x-axis, and reflecting about the y-axis.
Step 2 :To shift a function down by 9 units, we subtract 9 from the function. So, the new function becomes \(y=\sqrt{x}-9\).
Step 3 :Reflecting a function about the x-axis means changing the sign of the function. So, the new function becomes \(y=-(\sqrt{x}-9)\).
Step 4 :Reflecting a function about the y-axis means changing the sign of the variable inside the function. So, the new function becomes \(y=-\sqrt{-x}-9\).
Step 5 :However, it should be noted that the function \(y=-\sqrt{-x}-9\) is not defined for positive values of \(x\). This is because the square root of a negative number is not a real number. Therefore, the graph of the function only exists for \(x\leq0\).
Step 6 :\(\boxed{y=-\sqrt{-x}-9}\) is the function that is finally graphed after the transformations are applied to the graph of \(y=\sqrt{x}\).