### Home > APCALC > Chapter 1 > Lesson 1.2.1 > Problem1-24

1-24.

Sketch a graph of the piecewise-defined function $g ( x ) = \left\{ \begin{array} { l l } { 2 ^ { x } } & { \text { for } x \leq 2 } \\ { 3 x - 2 } & { \text { for } x > 2 } \end{array} \right.$.

1. State the domain and range of $g$.

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 $g$ continuous at $x = 2$? Explain.

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 $g$ continuous for all values of $x$?

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?

Click on the circles next to each equation in the eTool below to view it.
Click the link at right for the full version of the eTool: Calc 1-24 HW eTool