Answer:
Option C. [tex]y=-\sqrt{x-5}+3[/tex]
Step-by-step explanation:
The complete question in the attached figure
Remember that
The domain of the function are all possible values for variable x and the range of the function are all possible values for the variable y
Case A) we have
[tex]y=\sqrt{x-5}+3[/tex]
Remember that the discriminant must be greater than or equal to zero
For domain of this function
[tex](x - 5)\geq0\\x\geq5[/tex]
For range of the function
for every value of x ≥ 0
[tex]y\geq3[/tex]
Case B) we have
[tex]y=\sqrt{x+5}-3[/tex]
Remember that the discriminant must be greater than or equal to zero
For Domain
[tex](x + 5) \geq0\\x \geq(-5)[/tex]
and for every value of x ≥ (-5) range of the function will be
[tex]y \geq (-3)[/tex]
Case C) we have
[tex]y=-\sqrt{x-5}+3[/tex]
Remember that the discriminant must be greater than or equal to zero
For domain
[tex]x - 5 \geq 0\\x\geq 5[/tex]
For range
[tex]y \leq 3[/tex]
Case D) we have
[tex]y=-\sqrt{x+5}-3[/tex]
Remember that the discriminant must be greater than or equal to zero
For domain
[tex](x + 5) \geq 0\\x \geq -5[/tex]
For range
[tex]y \leq (-3)[/tex]
