8. Write the analytical expression of a function $f(x)$ that satisfies the following four conditions: $\qquad$
(1) The form of $f(x)$ is $f(x)=\frac{a_{2} x^{2}+b_{2} x+c_{2}}{a_{1} x^{2}+b_{1} x+c_{1}}$;
(2) $f(0)=-2, f(1)=-1$;
(3) For any $x$ in $[0,+\infty)$, $f(x)<0$;
(4) $f(x)$ is monotonically increasing on the interval $[0,+\infty)$.
8. $f(x)=-\frac{2}{x+1}$.

First, draw a rough graph based on conditions (2) (3) (4), resembling the graph of a reciprocal function. Set $y-b=\frac{k}{x-a}$, and determine the coefficients $a$, $b$, and $k$.