How do you graph #y=sqrtx-2# and what is the domain and range?

1 Answer
Feb 21, 2018

See below.

Explanation:

The graph looks like this:

graph{sqrt(x)-2 [-10, 10, -5, 5]}

The domain is all possible values of #x# that give out a defined value of #f(x)#.

Here, #y# will be undefined if #x<0#, as the square root function cannot, really, have an input below #0#

So #x>=0#.

In interval notation, the domain is #[0,oo)#.

The range is all possible outputs of #f(x)#.

Since a square root function does not give an answer above #0#, the range of #sqrt(x)# is #y>=0#. However, since the above function is #sqrt(x)-2#, the range is #y>=-2#, or in interval notation:

#[-2,oo)#.