Question

What is the range of the function `r(x) = sqrt(x - 10)`?

Answer 1

In this case you want to avoid a negative argument in your square root, so you set:
`x-10>=0`
and so: `x>=10` which represents the domain of your function.
The range will be all the `y>=0`. Regardless of the value of `x` you input in your function (as long as is `>=10`) the square root will always give you a POSITIVE answer or Zero.
Your function can have the value of `x=10` as minimum possible value giving you `y=0`. From there you can increase `x` up to `oo` and your `y` will increase as well (slowly).

graph{sqrt(x-10) [-5.33, 76.87, -10.72, 30.37]}