Question

Which function has a domain of x 25 and a range of y s3?

g= x-5+3
9 = x+5 -3
y=-x-5+3
y=-x+5 -3

Answer 1

`y = - √(x - 5) + 3`

Explanation:

The function
`y = - √(x - 5) + 3` has a domain x ≥ 5.

This is because the function remains real for (x - 5) ≥ 0 as negative within the square root is imaginary.

Hence, (x - 5) ≥ 0

⇒ x ≥ 5

Now, for all x values that are greater than equal to 5 the value of
`- √(x - 5)` will be negative.

So,
`- √(x - 5) \leq  0`

⇒
`- √(x - 5) + 3 \leq  3`

⇒ y ≤ 3

Therefore, the range of the function is y ≤ 3. (Answer)