# How do you graph y = abs(x+6)?

Apr 22, 2018

See explanation

#### Explanation:

Let's start by looking at its parent function: $y = \left\mid x \right\mid$
graph{|x| [-9.97, 10.03, -0.6, 9.4]}
Now looking at $y = \left\mid x + 6 \right\mid$ and the given transformation rules below...

...we can see the we must shift the entire graph $6$ units to the left

To do that, we take each point on the graph and subtract $6$ from the $x$ value.

For example:

The point $\left(0 , 0\right)$ shifted $6$ units to the left is:

$\left(0 \textcolor{b l u e}{- 6} , 0\right) \implies \left(- 6 , 0\right)$

Once we do that we'll get the following graph...
graph{|x+6| [-14.34, 5.66, -0.88, 9.12]}
...which is the graph of $y = \left\mid x + 6 \right\mid$