The red function is given by:
[tex]f(x)=\sqrt[]{x+3}-3[/tex]
Since it is the function:
[tex]\sqrt[]{x}[/tex]
Translated 3 units left and 3 units down.
The green function is:
[tex]g(x)=\sqrt[]{x-3}+3[/tex]
Since it is the function:
[tex]\sqrt[]{x}[/tex]
Translated 3 units right, and 3 units up.
