# How do you graph y=-abs(x+1)?

Jul 4, 2018

See below:

#### Explanation:

We understand the graph $y = | x |$ to be

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

What is different between $y = | x |$ and $y = - | x + 1 |$?

Well, we have a negative out front, so this represents a reflection over the $x$-axis. Our graph now looks like

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

What is the difference between $y = - | x |$ and $y = - | x + 1 |$?

graph{-|x+1| [-10, 10, -5, 5]}

Well, we have the plus one, which means our graph shifts one to the left. Putting all of this together, we get the graph of

$y = - | x + 1 |$

Notice, our graph is reflected over the $x$-axis, and shifted to the left by one.

Hope this helps!