Problem

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

Solution

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 :\(\boxed{\text{Final Answer: The final function after all transformations is } y=-\sqrt{x+4}-3. \text{ The graph of this function is a reflection of the graph of } y=\sqrt{x} \text{ about the x-axis, shifted down 3 units and left 4 units.}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/12502/

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