Question #04a42

1 Answer
Nov 25, 2017

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