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

$x - 10 \ge 0$
and so: $x \ge 10$ which represents the domain of your function.
The range will be all the $y \ge 0$. Regardless of the value of $x$ you input in your function (as long as is $\ge 10$) 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 $\infty$ and your $y$ will increase as well (slowly).