Answer
Refer to the sketch in the picture
Work Step by Step
$f(x,y)=\sqrt (x^2+y^2+1)$
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, $z=\sqrt (x^2+y^2+1)$
We need a set of values of $x,y$ which will help us find $z$
$x^2+y^2+1 \geq 0 => x^2+y^2\geq -1$
The domain of the function = {$x,y∈R$, and $x^2+y^2\geq -1$}
But $x, y$ can be any value since $x, y$ are squared and will produce a positive $z$ value
This information helps us to graph our function in three dimensions ($x,y,z$)
