Answer:
The function that has a domain of 'x' greater-than-or-equal-to 5 and a range of 'y' less-than-or-equal-to 3 is;
[tex]y = -\sqrt{x - 5} +3[/tex].
Step-by-step explanation:
The domain of a function are the possible 'x' values of the function
The range of a function are the possible 'y' values of the function
The given possible functions are;
1) [tex]y = \sqrt{x - 5} +3[/tex]
The range of values for the above function are;
Domain; x ≥ 5
Range; y ≥ 3
2) [tex]y = \sqrt{x + 5} -3[/tex]
The range of values for the above function are;
Domain; x ≥ -5
Range; y ≥ -3
3) [tex]y = -\sqrt{x - 5} +3[/tex]
The range of values for the above function are;
Domain; x ≥ 5
Range; y ≤ 3
4) [tex]y = -\sqrt{x + 5} -3[/tex]
The range of values for the above function are;
Domain; x ≥ -5
Range; y ≤ -3
Therefore, the required function is the third function, [tex]y = -\sqrt{x - 5} +3[/tex].
