The given function is
[tex]g(x)=|x|-1[/tex]
To graph these functions, we need to have a table where we can write down each coordinated pair. So what we're gonna do is to give arbitrary values to x, we'll replace those values in g(x), to obtain a value for y.
We are going to use the following domain subset:
[tex]x\colon\left\lbrace -2,-1,0,1,2\right\rbrace [/tex]
Let's replace each element into the function.
[tex]\begin{gathered} g(-2)=|-2|-1=2-1=1 \\ g(-1)=|-1|-1=1-1=0 \\ g(0)=|0|-1=0-1=-1 \\ g(1)=|1|-1=1-1=0 \\ g(2)=|2|-1=2-1=1 \end{gathered}[/tex]
These results allow us to build the following table.
x y
-2 1
-1 0
0 -1
1 1
Where each pair of numbers represents a point. Now, we just graph them on the coordinated system. The image below contains the graph of the given function.
