Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The function $y = - \sqrt{x - 5} + 3$ 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 $- \sqrt{x - 5}$ will be negative.

So, $- \sqrt{x - 5} \leq 0$

⇒ $- \sqrt{x - 5} + 3 \leq 3$

⇒ y ≤ 3

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