what is the domain, and range of the square root of x+7

Question

what is the domain, and range of the square root of x+7.

 

i know how to get the domain, but not the range. 

Answer 1

Since you said you know how to find the domain, we will start off by stating the domain is [-7, infinity). Now, for the range you must consider the possible values that the regular square root of x can give you.

 

Explicitly speaking, the square root function is assumed to return the positive root of a term. So the range, the possible values of y, is limited to positive numbers. And zero is possible with the square root of zero. So its range is [0, infinity).

 

For the problem at hand, the square root of x+7, the range is exactly the same as the graph is only shifted horizontally from the normal square root of x. So it's range is also [0, infinity)