There are 4 possible translations of the parent function [tex]f(x)=|x|:[/tex]
- a units to the right - the function will become [tex]f(x)=|x-a|;[/tex]
- a units to the left - the function will become [tex]f(x)=|x+a|;[/tex]
- a units up - the function will become [tex]f(x)=|x|+a;[/tex]
- a units down - the function will become [tex]f(x)=|x|-a.[/tex]
Now you have the function [tex]g(x)=-3+|x|=|x|-3[/tex] that is translated function [tex]f(x)=|x|[/tex] 3 units down.
Answer: correct choice is D
