Which function has a domain of x greater-than-or-equal-to 5and a range of y less-than-or-equal-to 3?
a. y = startroot x minus 5 endroot + 3
b. y = startroot x + 5 endroot minus 3
c. y = negative startroot x minus 5 endroot + 3
d. y = negative startroot x + 5 endroot minus 3

Option C.

y = negative StartRoot x minus 5 EndRoot + 3

Step-by-step explanation:

Domain and Range of Functions

Let's consider a function y=f(x) where x is a set of values such as f exists. All the values of x are called the domain of f. Similarly, f takes a set of values when x takes values in its domain. All the values f could take is its range

We know the domain and range of f are, respectively

Since all the options contain a square root, we already know the domain will be restricted by the argument of a square root, that is, it must be non-negative. From the given domain, we construct the argument of the square root

It corresponds to the argument of a square root that must be non-negative. So our function must contain

Now about the range, the square root is assumed as positive or zero, and the range is restricted as less or equal to zero, so we operate the inequality for y

Now we can safely say

Or equivalently

This corresponds to the option C. written as

a

step-by-step explanation: