解：?$(1)$?將點(diǎn)?$A$?代入?$y_1=\frac mx$?得，?$m=2$?
?$∴y_1=\frac 2x$?
將點(diǎn)?$B$?代入?$y_1=\frac 2x$?得，?$n=-1$?
將點(diǎn)?$A(1，$??$2)，$??$B(-2，$??$-1)$?代入一次函數(shù)表達(dá)式得
?$\begin{cases}k+b=2\\-2k+b=-1\end{cases} $?
∴一次函數(shù)的表達(dá)式為?$y_2=x+1$?
?$(2)$?由圖可得，當(dāng)?$x＜-2$?或?$0＜x＜1$?時，?$y_1＞y_2$?
?$(3)$?點(diǎn)?$C(0，$??$1)$?
?$S_{△AOC}=\frac 12×1×1=\frac 12$
?
