Given:
The parent function is
[tex]f(x)=x+6[/tex]
To find:
The equation of a function whose parent function, f(x)= x + 6, is shifted 4 units to the right.
Solution:
If parent function f(x) is shifted a units to the right to get the function g(x), then
[tex]g(x)=f(x-a)[/tex]
Here, a=4 units.
[tex]g(x)=f(x-4)[/tex]
[tex]g(x)=(x-4)+6[/tex] [tex][\because f(x)=x+6][/tex]
[tex]g(x)=x+2[/tex]
Therefore, the required function is [tex]g(x)=x+2[/tex] and option C is correct.
