Exercise 38 Page 161

First we will go through all the transformations from the graph of $f(x)=|x|$ to the graph of given function. After that we will make a table of values to graph this function.

Transformations

The given equation is a transformation of the parent function $f(x)=|x|.$ We can define each transformation from the inside to the outside. We will start with the transformation closest to $x$ and end with the farthest from $x.$ Let's review our function. To see how each of the transformations affects the parent function, it would be helpful to rewrite it first. This way we can look at each of the transformations individually and work our way from the inside to the outside.