Step 1

given:

the function \(\displaystyle{y}={\left|{x}\right|}-{2}\)

Step 2

as we know that if we have function y=f(x) then the equation of the function shifted at (h,k) is given by:

\(y-k=f(x-h)\)

the function \(\displaystyle{y}={\left|{x}\right|}-{2}\) can be rewritten as:

\(\displaystyle{y}={\left|{x}\right|}-{2}\)

\(\displaystyle{y}+{2}={\left|{x}\right|}\)

\(\displaystyle{y}-{\left(-{2}\right)}={\left|{x}\right|}\)

by comparing the equation obtained above with the equation y-k=f(x-h) it can be seen that

h=0

and k=-2

therefore it is the equation of the function \(\displaystyle{y}={\left|{x}\right|}\) which is shifted at (0,-2).

Step 3

therefore the graph of the function \(\displaystyle{y}={\left|{x}\right|}-{2}\) can be drawn by shifting the graph of the function \(\displaystyle{y}={\left|{x}\right|}\) at (0,-2).