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

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Answer 1 · 2018-07-04T20:13:58

See below:

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!

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