# How do you graph F(x,y)=sqrt(x^2+y^2-1)+ln(4-x^2-y^2)?

• Let $\Sigma$ the surface of your function $F$ : it's a surface of revolution because $F \left(x , y\right) = f \left(r\right)$ where $r = \sqrt{{x}^{2} + {y}^{2}}$. Precisely, $f \left(r\right) = \sqrt{{r}^{2} - 1} + \ln \left(4 - {r}^{2}\right)$
• First, plot the curve of $f : r \setminus \mapsto \sqrt{{r}^{2} - 1} + \ln \left(4 - {r}^{2}\right)$. You get
• Now, turn this curve around $z$-axes in 3D-space. You get the surface $\Sigma$