Problem $1$: $(6$ marks$)$ Choose two numbers a and $b$ between $0$ and $10.$ Sketch the graph of a function $f$ such that all the following conditions are fulfilled:

$($i$)F$ is continuous everywhere except at $x=$a and $x=b.$

$($ii$)\underset{xa}{lim}f(x)=1.$

$($iii$)\underset{x{b}^{+}}{lim}f(x)=-1$ and $\underset{x{b}^{-}}{lim}=2.$