Question

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

Answer 1

Answer:

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

$x\geq 5,\ y\leq 3$

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

$x\geq 5$

$x-5\geq 0$

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

$\sqrt{x-5}$

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

$y\leq 3\ =>\ 0\leq 3-y\ =>\ 3-y\geq 0$

Now we can safely say

$3-y=\sqrt{x-5}$

Or equivalently

$y=3-\sqrt{x-5}$

This corresponds to the option C. written as

$\boxed{y = negative StartRoot x minus 5 EndRoot + 3}$

Answer 2

Answer:

C. y = negative StartRoot x minus 5 EndRoot + 3

Step-by-step explanation: