# How do you graph the equation y= |x-2|-4?

Jul 2, 2017

graph{|x-2|-4 [-10, 10, -5, 5]}

#### Explanation:

We can easily graph the given function using translation properties of functions.

First, consider what the function $y = | x |$ actually means. It represents the absolute value, thus:

$| x | = \left\{\begin{matrix}- x & x < 0 \\ 0 & x = 0 \\ x & x > 0\end{matrix}\right.$

And its graph is therefore:

graph{|x| [-10, 10, -5, 5]}

So then the graph of $y = | x - 2 |$ is the same as the above graph except that it is translated right by $2$ units

graph{|x-2| [-10, 10, -5, 5]}

Then finally the graph of $y = | x - 2 | - 4$ is the same as the above graph except that it is translated down by $4$ units

graph{|x-2|-4 [-10, 10, -5, 5]}