Question

Question #04a42

Answer 1

`2>=y>=0`

Explanation:

The range of a function is the range of values which the function can take given it's domain.
As the domain is not given, assume that it is all values of x which give a real y (in this case `|\x|<=2`).

Three important facts to remember in this question are that:
a) you can only take the square root of a positive number
b) `y=sqrt(f(x))` only plots the positive square root (principal root)
c) any real number squared `>=0`

Using a), you know `4-x^2>=0`. Because of c), the maximum value `4-x^2` can take is 4, when `x=0`, so the maximum value of y is `sqrt(4)=2`.
Using a) the minimum value `4-x^2` can take is 0, when `x=+-2`, and `sqrt(0)=0`.

Given the minimum and maximum it follows that `0<=x<=2`