Vertical translations occur outside the absolute value while horizontal translations occur inside the absolute value.
Practice makes perfect
We are asked to graph the equation y=|x|-3 by translating the graph of y=|x|. When translating absolute value functions, vertical translations occur after evaluating the absolute value. Consider the following general equation, where k is a positive number.
y=|x|- k
The graph of this equation is a vertical translation of the graph of y=|x| down k units. Let's start with the graph of the parent function y=|x|.
In the case of the given function, k is equal to 3. Therefore, the transformation will move the graph of y=|x| down by 3 units. As an example, we will translate three points on the graph of y=|x| down by 3 units.
Translating each and every point 3 units down means shifting the entire graph of y=|x| down by 3 units.
