Exercise 40 Page 549

We want to describe the transformations of the parent function $f(x)=\sqrt{x}$ represented by $h(x)=\text{-}\sqrt{x-3}-2.$

Identifying the Transformations

Let's look at the possible transformations. Then we can more clearly identify the ones being applied.

Transformations of $f(x)$
Vertical Translations	$$\begin{array}{c}\text{Translation up }k\text{ units, }k>0\\ y=f(x)+k\end{array}$$
	$$\begin{array}{c}\text{Translation down }k\text{ units, }k>0\\ y=f(x)-k\end{array}$$
Horizontal Translations	$$\begin{array}{c}\text{Translation right }h\text{ units, }h>0\\ y=f(x-h)\end{array}$$
	$$\begin{array}{c}\text{Translation left }h\text{ units, }h>0\\ y=f(x+h)\end{array}$$
Reflections	$$\begin{array}{c}\text{In the }x\text{-axis}\\ y=\text{-}f(x)\end{array}$$
	$$\begin{array}{c}\text{In the }y\text{-axis}\\ y=f(\text{-}x)\end{array}$$

Now, using the table, let's highlight the transformations.