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| according to the given transformation. When translating absolute value functions, verticaltranslations occur after the absolute value has been evaluated. This is why they are outside the absolute value symbols. Consider the following general equation, where k is a real number.
y=|x|+ k
The graph of this equation is a vertical translation of y=|x| by k units. Let's start with the graph of y=|x|.
Let's review our given function.
y=|x|+ 3
In this case, k is equal to 3. Since we are adding a positive value, the transformation will move the graph of y=|x| up by 3. As an example, we will translate three points on the graph of y=|x| up by 3 units.
Translating each and every point 3 units up means shifting the entire graph of y=|x| up by 3 units.
