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

1 Answer
Jul 4, 2018

Answer:

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!