Chapter 2.5, Problem 28AYU

In Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of $y\text{ = }\sqrt{x}$ in the order stated.

(1) Reflect about the $x\text{-axis}$

(2) Shift right 3 units

(3) Shift down 2 units

To determine

To find: The function that is finally graphed after each of the following transformations is applied to the graph of $y=\sqrt{x}$ in the order stated.

1. Reflect about the $x\text{-axis}$.

Answer to Problem 28AYU

$y=-(\sqrt{x-3})-2$

Explanation of Solution

Given:

$y=\sqrt{x}$

Step 1: Reflect about the $x\text{-axis}$.

Multiply by $-1$ on the function $y=\sqrt{x}$.

We get, $y=-\sqrt{x}$.

To determine

To find: The function that is finally graphed after each of the following transformations is applied to the graph of $y=\sqrt{x}$ in the order stated.

2. Shift right 3 units.

Answer to Problem 28AYU

$\underset{\_}{y=-(\sqrt{x-3})-2}$

Explanation of Solution

Given:

$y=\sqrt{x}$

Step 2: Shift right 3 units.

Replace $x$ by $x-\text{ 3}$ on the function $y=-\sqrt{x}$.

$y=-(\sqrt{x-3})$

To determine

To find: The function that is finally graphed after each of the following transformations is applied to the graph of $y=\sqrt{x}$ in the order stated.

3. Shift down 2 units.

Answer to Problem 28AYU

$\underset{\_}{y=-(\sqrt{x-3})-2}$

Explanation of Solution

Given:

$y=\sqrt{x}$

Step 3: Shift down 2 units.

Subtract 2 from $y=-(\sqrt{x-3})$.

$y=-(\sqrt{x-3})-2$