the range of a function?

Question

what is the range of the function?

r(x) = Square of(x - 10)

Answer 1

Do you mean square -root?
if so, the answer is easy.
when you have a function under a square-root, you should take care of the function not to accept a value less than zero, as you always do.
now there is a nice solution for finding the range of this function:
try to calculate x as a function of y (or r)
then the domain of the new function will be the desired range! Look:

r(x) = Square of(x - 10) , notice that r(x) is always equal or more than zero it means r>=0 (***)

r(x) = Square of(x - 10) then
r^2=x-10
r^2+10=x
now you might say that the domain of the new function is IR, but you should consider (***) so the r has always positive values(equal or more than zero) so the domain is r>=0 and this also the range of the main function, if you plot the diagram you can understand it better.

Answer 2

The range is all real numbers greater than or equal to zero. A squaring operation on a real value can never result in a negative value. But r(10) = (10 - 10)^2 = 0^2 = 0, and r(x) can take on any value larger than this as well.

Answer 3

The function has its minimum value of 0 when x=10. Its range is the nonnegative reals (x>=0)