Find the function that is finally graphed after the following transformations are applied to the graph of $y=\sqrt{x}$ in the order listed.
(1) Reflect about the $x$-axis
(2) Shift down 3 units
(3) Shift left 4 units
Answer
\(\boxed{\text{Final Answer: The final function after all transformations is } y=-\sqrt{x+4}-3. \text{ The graph of this function is a reflection of the graph of } y=\sqrt{x} \text{ about the x-axis, shifted down 3 units and left 4 units.}}\)
Step 1 ：The transformations applied to the function \(y=\sqrt{x}\) are as follows:
Step 2 ：1) Reflect about the x-axis: This changes the function to \(y=-\sqrt{x}\).
Step 3 ：2) Shift down 3 units: This changes the function to \(y=-\sqrt{x}-3\).
Step 4 ：3) Shift left 4 units: This changes the function to \(y=-\sqrt{x+4}-3\).
Step 5 ：\(\boxed{\text{Final Answer: The final function after all transformations is } y=-\sqrt{x+4}-3. \text{ The graph of this function is a reflection of the graph of } y=\sqrt{x} \text{ about the x-axis, shifted down 3 units and left 4 units.}}\)
