Answer:
Domain (-inf,9]
Range [-2,inf)
Step-by-step explanation:
The domain is every real number that x can be so that y is also real.
9-x has to be positive or zero in order for the square root of it to be real.
So we must solve 9-x>=0.
Add x on both sides: 9>=x
So x is any real number smaller than or equal to 9.
Interval notation (-inf,9]
The range represents all the y values obtained from plugging in our domain.
y=sqrt(9-x)-2
So sqrt(9-x) is either 0 or positive which means the smallest value y is 0-2=-2. So the range is every real number equal to -2 or greater.
Interval notation: [-2,inf)
