Exercise 29 Page 17

To write the function rule $g(x),$ let's look at possible transformations. Then we can more clearly decide which operations should be used to apply the desired transformations to the parent function.

Transformations of $f(x)$
Horizontal Translations	$$\begin{array}{c}\text{Translation right }h\text{ units, }h>0\\ y=f(x-h)\end{array}$$
	$$\begin{array}{c}\text{Translation left }h\text{ units, }h>0\\ y=f(x+h)\end{array}$$
Horizontal Stretch or Shrink	$$\begin{array}{c}\text{Horizontal stretch, }b>1\\ y=f\left(\frac{1}{b}x\right)\end{array}$$
	$$\begin{array}{c}\text{Horizontal shrink, }0<b<1\\ y=f\left(\frac{1}{b}x\right)\end{array}$$

Using the table, let's apply the first transformation, a translation $2$ units to the right, by substituting $(x-2)$ for each $x\text{-}$term.