what is the range of the function ( y = sqrt{x + 5} )?\n( ygeq - 5 )\n( ygeq 0 )\n( ygeqsqrt{5} )\n( ygeq 5 )

Explanation:

Step1: Recall the property of square - root functions

For a square - root function (y = \sqrt{u}), the value of (y) is non - negative because the square root of a real number (u) (where (u\geq0)) is defined as a non - negative real number. In the given function (y=\sqrt{x + 5}), let (u=x + 5).

Step2: Determine the range

Since the square root function (y=\sqrt{u}) (here (u=x + 5)) has the property that (y\geq0) for all real values of (x) that make (u=x + 5\geq0) (the domain condition for the square root function). The output of the square - root operation (\sqrt{x+5}) is always greater than or equal to (0).

Answer:

(y\geq0)