Question

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

Answer 1

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!