Exercise 13 Page 16

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.

Reflections
$$\begin{array}{c}\text{In the }x\text{-axis}\\ y=\text{-}f(x)\end{array}$$	$$\begin{array}{c}\text{In the }y\text{-axis}\\ y=f(\text{-}x)\end{array}$$

Using the table, let's apply the given transformation, a reflection in the $y$-axis, by substituting $\text{-}x$ for each $x$ in the equation. Next, we can replace $f(\text{-}x)$ with $g(x)$ and complete the function rule. Notice that in this case reflection in the $y\text{-}$axis did not change the function rule, because this function has an axis of symmetry exactly on the $y\text{-}$axis.

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.