# Question #615a6

Feb 24, 2018

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

#### Explanation:

We know that for the parent function of a radical, $\sqrt{x}$, the domain is $\left(0 , \infty\right)$ since we can't put a negative number under the radical.
For this function, since we need a domain of $\left[3 , \infty\right)$, we can just put $x - 3$ under the radical. For any value smaller than three, we get a negative number under the radical.

Now the range: The range of the parent function is $\left(0 , \infty\right)$ since we can't take a square root and end up with anything less than $0$. We need to reverse this so it's $\left(- \infty , 0\right]$. Reflect the function over the $y$-axis by putting a negative sign in front of the radical.
So we end up with $y = - \sqrt{x - 3}$

I hope that helps!