$(14$ points$)$ Given $f(x)=\frac{1}{2x}$

a$)$ Sketch a graph of this function.

b$)$ What is the Domain and Range of this function?

c$)$ Find $\underset{x{0}^{+}}{lim}f(x)=,\underset{x{0}^{-}}{lim}f(x)=$

d$)$ Does $\underset{x0}{lim}f(x)$ exist? Explain.

e$)$ Find $f(0).$

f$)$ Determine if $f(x)$ is continuous at $x=0.$ Explain.