Answer
Refer to the sketch in the picture
Work Step by Step
$f(x,y)=\sqrt (9 - x^2 - y^2)$
In order to draw the graph we need to know the number of independent variables ($n$), which will help us figure out the number dimensions needed to draw the graph.
The function has two independent variables $x,y$
The dimension ($m$) = $n+1$
Hence we need three dimensions, that is, $x,y,z$
But the third dimension is the value of the function, that is, $z=\sqrt (9 - x^2 - y^2)$
We need a set of values of $x, y$ which will help us find $z$
[NB: There should no negative values under the square root, hence the values of x and y selected must not give a negative number under the square root]
Finding the range of values we need in plotting our graph
$9-x^2-y^2\geq0$
$-x^2-y^2\geq-9$ or
$x^2+y^2\leq9$ hence the values of $x,y$ are restricted a particular domain
This information helps us to graph our function in three dimensions ($x,y,z$)
