Answer
Refer to the sketch in the picture
Work Step by Step
$f(x,y)=x^2+y^2$
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, $z=x^2+y^2$
We need a set of values of $x,y$ which will help us find $z$
The domain of the function = {$x, y \in R$} Hence $x, y$ can be any value
This information helps us to graph our function in three dimensions ($x,y,z$)