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.

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

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

   Hint (b):

   

3. $g(x)$ 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.