Exercise 21 Page 17

First, we will take a look at the given graph.

As we can see, each $y\text{-}$value of $f$ is multiplied by $\frac{1}{2}$ - this is a vertical shrink. To write the function rule $g(x),$ let's look at a table.

Vertical Stretch or Shrink
$$\begin{array}{c}\text{Vertical stretch, }a>1\\ y=af(x)\end{array}$$	$$\begin{array}{c}\text{Vertical shrink, }0<a<1\\ y=af(x)\end{array}$$

Using the table, let's apply the given transformation. It is a vertical shrink by a factor of $\frac{1}{2},$ so we will multiply both sides of the equation by $\frac{1}{2}.$ Next, we can replace $\frac{1}{2}f(x)$ 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.