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(a) If $c>0$, $f(x,y,z)=c$, i.e. $x^2+y^2+z^2=c$, is the sphere of radius $\sqrt{c}$ centered at the origin. If $c=0$, $f(x,y,z)=c$ is just the origin. If $c<0$, no $(x,y,z)$ satisfies $f(x,y,z)=c$.

(b) $f(x,y,z)=c$, i.e. $x+2y+3z=c$, is the plane normal to $(1,2,3)$ passing through $(c,0,0)$.

(c) If $c>0$, $f(x,y,z)=c$, i.e. $x^2+y^2=c$, is the cylinder parallel to the $z$-axis whose cross-section is a circle of radius $\sqrt{c}$ that is parallel to the $xy$-plane and is centered on the $z$-axis. If $c=0$, $f(x,y,z)=c$ is the $z$-axis. If $c<0$, no $(x,y,z)$ satisfies $f(x,y,z)=c$.