What is the domain and range of f(x) = sqrt (9 - x^2)?

1 Answer
Aug 12, 2017

Domain: [-3,3]
Range: [0,3]

Explanation:

The value under a square root cannot be negative, or else the solution is imaginary.

So, we need 9-x^2\geq0, or 9\geqx^2, so x\leq3 and x\geq-3, or [-3.3].

As x takes on these values, we see that the smallest value of the range is 0, or when x=pm3 (so sqrt(9-9)=sqrt(0)=0), and a max when x=0, where y=\sqrt(9-0)=sqrt(9)=3