Chapter 2.5, Problem 27AYU

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) Shift up 2 units

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

(3) Reflect about the $y\text{-axis}$

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. Shift up 2 units.

Answer to Problem 27AYU

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

Explanation of Solution

Given:

$y=\sqrt{x}$

Step 1: Shift up 2 units.

add 2 from each $y\text{-coordinates}$ on the function $y=\sqrt{x}$.

We get, $y=\sqrt{x}+2$.

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

Answer to Problem 27AYU

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

Explanation of Solution

Given:

$y=\sqrt{x}$

Step 2: Reflect about the $x\text{-axis}$.

Multiply by $-1$ on the function $y=\sqrt{x}+2$.

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

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. Reflect about the $y\text{-axis}$.

Answer to Problem 27AYU

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

Explanation of Solution

Given:

$y=\sqrt{x}$

Step 3: Reflect about the $y\text{-axis}$.

Replace $x$ by $-x$ on the function $y=-(\sqrt{x}+2)$.

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