Answer:
C. [tex]y=\sqrt{2x-6}+1[/tex]
Step-by-step explanation:
From the graph of the function, we can see that the domain of the function is [tex]x\ge 3,[/tex] the range of the function is [tex]y\ge 1.[/tex]
Consider the parent function [tex]y=\sqrt{x}.[/tex]
The domain of this function is [tex]x\ge 0,[/tex] the range of this function is [tex]y\ge 0.[/tex]
The function [tex]y=\sqrt{2x-6}+1[/tex] has
the domain
[tex]2x-6\ge 0\\ \\2x\ge 6\\ \\x\ge 3[/tex]
and the range
[tex]y\ge 0+1\\ \\y\ge 1[/tex]
All other options have different domain, or the range, or both the domain and the range.
