QuestionTrace the level sets for these functions:
1. $f(x, y)=x-y$
2. $f(x, y)=xy$
3. $f(x, y)=\arcsin\left(\frac{y}{x}\right)$
4. $f(x, y)=e^{y-x^{2}}$
5. $f(x, y, z)=x^{2}-2x+y^{2}+z^{2}+1$

Studdy Solution
Rearranging terms, we get$$x^{}-x+y^{}+z^{} = c -$$Completing the square for $x$, we get$$(x-)^{}+y^{}+z^{} = c -$$This is the equation of a sphere with center at $(,0,0)$ and radius $\sqrt{c-}$. As $c$ varies, we get a family of spheres.