CPM Homework Help : CALC Problem 1-24

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

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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.

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.

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?