Use the graph of $g(x)$ below to answer the following questions. Provide reasons for each value found.

1. For what values of $x$ is $g(x)$ undefined?

   Hint (a):

   Are there any $x$ values for which there is no existing $y$-value?

2. For what values of $x$ is $g(x)$ discontinuous?

   Hint (b):

   There are three conditions of continuity.
   If any of these conditions are violated, then the function is NOT continuous at the value of $x$.
   1. $\lim\limits_{x\rightarrow a}g(x)$ exists. This means that $\lim\limits_{x\rightarrow a^{-}}g(x)=\lim\limits_{x\rightarrow a^{+}}g(x)$ and that limit is finite.
   2. f(a) exists. This means that f(a) is finite.
   3. $\lim\limits_{x\rightarrow a}g(x)=f(a)$

   Answer (b):

   $y = g(x)$ has exactly three points in which it is discontinuous. Where are they?

3. For what values of $x$ is $g(x)$ non-differentiable?

   Hint (c):

   A function is NOT differentiable where it is not continuous and/or where the derivative is not continuous. Examples of points of non-differentiablity include: cusps, endpoints, jumps, holes and vertical tangents.