Exercise 2 Page 348

Let's recall what we know about horizontal and vertical translations of a graph of an absolute value function. Remember that a translation does not change the graph, it shifts the graph in vertical, horizontal or in both directions. Let's look at the graph of a function $y=|x|.$

We will start with the vertical translation. For an example, we would like to translate the graph of the function $y=|x|$ $1$ unit down. Keep in mind that vertical translation occurs outside the absolute value. When translating $\text{down}$ we need to $\text{subtract}$ the value. Let's take a look at the translated graph. Next, we will focus on the horizontal translation. Let's see what happens when we want to translate a graph of $y=|x|-1$ $3$ units left. The most important thing to remember is that horizontal translation occurs inside the absolute value. When translating $\text{left}$ we need to $\text{add}$ the value. Now, let's take a look at the graph after two translations, the first one unit down and the second one, three units left.