# What is the domain and range if the function #f(x)= sqrt(4-x^2)#?

##### 2 Answers

Your domain is all the legal (or possible) values of

**Domain**

The domain of a function includes every possible value of *negative*. Because there is no denominator, you will never divide by zero. What about complex numbers? You have to set the inside of the square root to less than zero and solve:

So your domain is

**Range**

Your range is partly determined by your legal values of

graph{sqrt(4-x^2) [-2.1,2.1,-1,2.5]}

This is the top half a circle and the range is

{x

{y

Because of the radical sign, for f(x) to be a real function,

{y