Question

How do you find the domain and range of `f(x) = sqrt(4 - x²)`?

Answer 1

Domain: `-2<=x<=2`;
Range: `0<=y<=2`

Explanation:

You want to avoid to have a negative number as argument of your square root, so you must set:
`4-x^2>=0` that can be rearranged to get (changing signs):
`x^2<=4`
`x<=+-sqrt(4)`
`x<=+-2`
So, basically, your function can accept only `x` values inside the interval from `-2` to `+2` giving a domain: `-2<=x<=2`.
The maximum `y` value of your function is reached when `x=0` and corresponds to `y=2`. So the range will be from `0` to `+2` or: `0<=y<=2`

Graphically:
graph{sqrt(4-x^2) [-10, 10, -5, 5]}