Question

Find the domain and the range of the function
h(x)=sqrt(9-x^2)
answer using interval notation please

Answer 1

for domain solve
\[9-x^2\geq 0\] or note that this function represents the upper half of a circle with radius 3 centered at the origin

Answer 2

if that is not clear, start with
\[x^2+y^2=3^2\] the entire circle
solve for \(y\) and get
\[y=\pm\sqrt{9-x^2}\]
since you don't have the \(\pm\) part this is the upper half of the circle

Answer 3

that makes the domain \([-3,3]\)