Question

What is the domain and range of the function `f(x) =sqrt(x-9)`?

Answer 1

Domain: `(-oo, 9) uu (9, oo)`
Range: `(0, oo)`

Explanation:

Domain:
Domain = x-values

When we find the domain of a root, we first have to set it to `cancel>=0`, as a root of something can't be a negative number. So the restriction for the domain looks like this:
`sqrt(x-9) cancel>=0` simplify:
`x-9 cancel>=0`
`x cancel>=9` So if you write the domain in interval notation, it looks like this:
`(-oo, 9) uu (9, oo)`

Range:
Range = y-values
The range of a square root function is `>0`
So if you write the range in interval notation, it looks like this:
`(0, oo)`