What is the domain and range of y=sqrt(4-x^2) ?
2 Answers
Domain:
Explanation:
Start by solving the equation
4 - x^2 = 0
Then
(2 + x)(2 -x) = 0
x = +- 2
Now select a test point, let it be
Thus, the graph of
Hopefully this helps!
Range:
Explanation:
The domain has already been determined to be
y=sqrt(4-x^2)=(4-x^2)^(1/2)
dy/dx=1/2(4-x^2)^(-1/2)d/dx(4-x^2)=1/2(4-x^2)^(-1/2)(-2x)=(-x)/sqrt(4-x^2)
Thus the range is
We could also arrive at this conclusion by considering the graph of the function:
y^2=4-x^2
x^2+y^2=4
Which is a circle centered at
Note that solving for
Thus