Data 605 Discussion 16

In Exercises 7 – 14, give the domain and range of the multi-variable function.

\[\ f(x, y) = \sqrt{9-x^2-y^2}\]

\[\ 0 \leq 9-x^2-y^2\]

\[\ x^2-y^2 \leq 9\] Domain

\[\ D = {(x,y) x^2-y^2 \leq 9} \] Square root ensures that all output is \(\ \geq0\).

\(\ x = 0, y = 0\)

\(\ f(0, 0) = \sqrt{9-(0)^2-(0)^2}\)

\(\ f(0,0) = 3\)

Therefore the range R is the interval [0,3]