8. If one edge length of a tetrahedron is $x$, and the other edges are all 1, the volume is $F(x)$, then the function $F(x)$ on its domain
(A) is an increasing function but has no maximum value
(B) is an increasing function and has a maximum value
(C) is not an increasing function and has no maximum value
(D) is not an increasing function but has a maximum value
(D)
8.【Analysis and Solution】In tetrahedron $ABCD$, let $AB=x$, $AC=AD=BC=BD=CD=1$. Fix $\triangle BCD$ as the base, with all three sides being 1, and its area is $\frac{\sqrt{3}}{4}$, a constant. As $\triangle ACD$ rotates around $CD$, the value of $x$ changes, and the height from $A$ to the base, $AO$, also changes. This indicates that the domain of $F(x)$ is $(0, \sqrt{3})$.
Let $AO=h$. The volume of the tetrahedron, when $S_{\triangle BCD}=\frac{\sqrt{3}}{4}$, depends on the changes in $h$. As $x \rightarrow 0$ or $x \rightarrow \sqrt{3}$, $F(x) \rightarrow 0$, so $F(x)$ is not an increasing function.
When plane $ACD \perp$ plane $BCD$, $h$ reaches its maximum value, at which point $F(x)$ reaches its maximum value. Therefore, $F(x)$ is not an increasing function but has a maximum value.