What is the range of the function y = square root x+5?

To determine the range of this function, we must first evaluate the domain. The square root function is a nice, neat function as long as the radicand isn’t negative. In this function, the radicand becomes negative after x gets smaller than - 5, so the domain of this function is [-5, infinity).

Now that we know the domain, we can calculate the range. Beginning with the left boundary, we can substitute - 5 into the function to see what y equals at this x-value. At - 5, y equals 0, so the minimum value for the range is 0; with the right boundary, substituting infinity yields infinity, so the range is any number greater than 0.

D: x> = - 5

R: y>=0