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

1 Answer
Shantelle
Oct 14, 2017

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)

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