Exercise 36 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. First, there is a horizontal translation $1$ units to the left, $\left|x\right|\Rightarrow \left|x+1\right|.$ Remember, typically $|x-h|$ is a horizontal translation $h$ units to the right, while $|x+h|$ is translated $h$ units to the left.