Question

Consider the real function g with rule g(x)=
`√(9-x) -2` .Use interval notation to describe the domain and range of g.

Answer 1

Domain (-inf,9]

Range [-2,inf)

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)