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Some level sets of $x_3-x_1^2-x_2^2$

According to the book (Simon and Blume - Math for Economics) level sets of multivariable function could be sketched solving the equation $z=f(x_1,x_2,x_3)$ for $x_3$ in terms of the other variables: $x_3=g(x_1,x_2)$ and then graph g using the techniques for graphing functions of two variables. For the abovementioned picture, we have to write $z=0$ and draw the graph of $x_3=x_1^2+x_2^2$. You get one graph, but why those graphs are drawn like in the picture ?

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    Because that's what $z = x_1^2 + x_2^2$ and $z = x_1^2 + x_2^2 - 3$ and so on look like. – 2017-01-09

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This picture does not only picture the $z=0$ levelset, but also the (I'd guess) the $z=1$ and $z=2$ levelsets. So you get the three graphs \begin{align*} x_3 &= x_1^2+x_2^2 \\ x_3 &= x_1^2 +x_2^2 -1\\ x_3 &= x_1^2+ x_2^2 -2 \end{align*}