Question

Question #615a6

Answer 1

`y=-sqrt(x-3)`

Explanation:

We know that for the parent function of a radical, `sqrt x`, the domain is `(0,oo)` since we can't put a negative number under the radical.
For this function, since we need a domain of `[3,oo)`, 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 `(0,oo)` since we can't take a square root and end up with anything less than `0`. We need to reverse this so it's `(-oo,0]`. 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!