The answer depends on the domain.
If the domain is non-negative real numbers, then the range is the whole of the real numbers.
If the domain is the whole of the real numbers (or the complex plane) , the range is the complex plane.
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If the range is the real numbers, it has a lower bound (zero) but no upper bound.
This is because the square root function, with the range defined as the non-negative real numbers, is monotonic increasing throughout.
yes
"Domain" means for what numbers the function is defined (the "input" to the function). For example, "x + 3" is defined for any value of "x", whereas "square root of x" is defined for non-negative "x". "Range" refers to the corresponding values calculated by the function - the "output" of the function. If you write a function as y = (some function of x), for example y = square root of x, then the domain is all possible values that "x" can have, whereas the range is all the possible values that "y" can have.
Yes, if your equation is f(x) = sqrt5(x). The square root is also a function itself, if that's what you mean.