Exercise 2 Page 13

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.

Horizontal Translations
$$\begin{array}{c}\text{Translation right }h\text{ units, }h>0\\ y=f(x-h)\end{array}$$	$$\begin{array}{c}\text{Translation left }h\text{ units, }h>0\\ y=f(x+h)\end{array}$$

Using the table, let's apply the given transformation, a translation $4$ units to the right, by substituting $(x-4)$ for each $x\text{-}$term. Next, we can replace $f(x-4)$ with $g(x)$ and complete the function rule.

Checking the Answer

To verify your answer, enter the function rules in the calculator by pushing $\boxed{\text{Y}=}$ and writing them in the first and second rows. Next, by pushing $\boxed{\text{GRAPH}},$ the calculator will draw the graphs of the functions.

Looking at the graph, we can confirm that our solution is correct.