Sketch the graph of the piecewise function $g(x)$ below. .

$g ( x ) = \left\{ \begin{array} { l l } { 2 ^ { x } } & { \text { for } x \leq 2 } \\ { 3 x - 2 } & { \text { for } x > 2 } \end{array} \right.$

1. State the domain and range of $g(x)$.

   Hint (a):

   Consider the domain and range of each piece separately . Then combine.
   Domain: Both $2^x$ and $3x - 2$ have a domain of all real numbers.
   Range: $2^x$ on $x ≤ 2$ has a range of $0 < y ≤ 4$ and $3x - 2$ on $x > 2$ has a range of $4 < y$.

2. Is $g(x)$ continuous at $x = 2$? Explain.

   Hint (b):

   Later in this course we will learn a formal definition of continuity. For now, think about what continuous means to you. Now look at the graph at $x = 2$. Make a conclusion and justify.

3. Is $g(x)$ continuous on all values of $x$?

   Hint (c):

   Consider other values of $x$, other than $x = 2$. Is the function continuous at these point? Is there anywhere where the function will not be continuous?