For each part below, draw a graph of a function that meets the given conditions, if possible. If such a function is not possible, explain why not.

1. $g$ is discontinuous at $x = a$, but $\lim\limits _ { x \rightarrow a } g ( x )$exists.

   Hint (a):

   $\lim\limits_{x\rightarrow a }f(x)\text{ exist if: }\lim\limits_{x\rightarrow a^{-} }f(x)=\lim\limits_{x\rightarrow a^{+} }f(x)$

2. $g$ is continuous at $x = a$, but $\lim\limits _ { x \rightarrow a } g ( x )$ does not exist.

   Hint (b):

   Check the 3 conditions for continuity.

3. $g$ is discontinuous at $x = a$, and $\lim\limits _ { x \rightarrow a } g ( x )$ does not exist.

   Hint (c):

   Limits exist when both sides approach the same finite value. What does it mean for a limit to not exist?