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

1 Answer
Oct 14, 2017

Answer:

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)#