Answer:
The correct option is C) [tex]g(x)=|x-1|+3[/tex].
Step-by-step explanation:
Consider the provided graph:
The Parent Function for the provided graph is [tex]|x|[/tex].
The graph of [tex]|x|[/tex] is shifted 3 unit up and 1 unit right to the origin.
For a function [tex]g(x)=f(x)+k[/tex] the function [tex]f(x)[/tex] shift k units up.
For the function [tex]g(x)=f(x-h)[/tex] the function [tex]f(x)[/tex] shift h units right.
As we know the graph has been shifted shifted 3 unit up and 1 unit right to the origin.
Therefore, the required equation is:
[tex]g(x)=|x-1|+3[/tex]
Hence, the correct option is C) [tex]g(x)=|x-1|+3[/tex].
