Question

How do you write `g(x) = |2 + x| - 1` as piecewise functions?

Answer 1

Check below.

Explanation:

If `x+2>0` , `g(x)=x+2-1=x+1`

If `x+2<0` , `g(x)=-x-2-1=-x-3`

`g(x) = {(x+1", "x> -2),(-x-3" , "x<=-2):}`

graph{|x+2|-1 [-10, 10, -5, 5]}

You can tell from the graph it's `y=x` shifted 1 point upwards and `y=-x` shifted 3 points downwards.