Letter B$,$ C$,$ and D

Sketch a graph of a function with the following characteristics $($four different graphs, one for each of the parts A$-$D$),$ or explain why such a function$/$graph is not possible.

A$)$ Dom$(f)$:$(-,2)(2,)($the domain of the function$)$

$f(1)=0$

$\underset{x{2}^{-}}{lim}f=$

$\underset{x2}{lim}f$ Does Not Exist

$\underset{x-}{lim}f=-2$

for $x>2,f<mn>0</mn>$

B$)f$ has a jump discontinuity at $x=1$ where $\underset{x{1}^{-}}{lim}f=-(\underset{x{1}^{}}{lim}f)$

$\underset{x}{lim}f=0$

$\underset{x-}{lim}f=$

$f(x)=0$ has no real solution

C$)$ Dom$(f)$:$(0,)($the domain of the function$)$

Ran$(f)$:$(-,),($the range of the function$)$

$f$ has a removable discontinuity at $x=3$ where $f(3)=2(\underset{x3}{lim}f)$

$f(x)=0$ has exactly three real solutions

D$)f$ is continuous on $(-,)$

$\underset{x}{lim}f=5$ and $f$ crosses this horizontal asymptote exactly twice

$f(0)=-1$

$f(x)=1$ has no real solution

Sketch a graph of a function with the following characteristics $($four different graphs, one for each of the parts A$-$D$),$ or explain why such a function$/$graph is not possible.

A$)$ Dom$(f)$:$(-,2)(2,)($the domain of the function$)$

$f(1)=0$

$\underset{x{2}^{-}}{lim}f=$

$\underset{x2}{lim}f$ Does Not Exist

$\underset{x-}{lim}f=-2$

for $x>2,f<mn>0</mn>$

B$)f$ has a jump discontinuity at $x=1$ where $\underset{x{1}^{-}}{lim}f=-(\underset{x{1}^{}}{lim}f)$

$\underset{x}{lim}f=0$

$\underset{x-}{lim}f=$

$f(x)=0$ has no real solution

C$)$ Dom$(f)$:$(0,)($the domain of the function$)$

Ran$(f)$:$(-,),($the range of the function$)$

$f$ has a removable discontinuity at $x=3$ where $f(3)=2(\underset{x3}{lim}f)$

$f(x)=0$ has exactly three real solutions

D$)f$ is continuous on $(-,)$

$\underset{x}{lim}f=5$ and $f$ crosses this horizontal asymptote exactly twice

$f(0)=-1$

$f(x)=1$ has no real solution