Let $g ( x ) = \left\{ \begin{array} { l l l } { 2 } & { \text { for } } & { 0 \leq x \leq 3 } \\ { 3 } & { \text { for } } & { 3 < x \leq 5 } \\ { 7 } & { \text { for } } & { 5 < x \leq 8 } \end{array} \right.$.          

1. Sketch the graph of $y = g(x)$. Is this function continuous?

   Hint (a):

   Continuous functions must have connected pieces. There can be no jumps or holes. What happens to $g(x)$ at $x = 3$ and at $x = 5$?

2. Shade the area between $g$ and the $x$-axis. What is the shaded area?

   Hint (b):

   Area of Rectangle A: $2 × 3 = 6$ units²
   Area of Rectangle B: $3 × 2 = 6$ units²
   Area of Rectangle C: $7 × 3 = 21$ units²

   Answer (b):

   $\text{Rectangle A} + \text{Rectangle B} + \text{Rectangle C} = 33 \text{ units}^{2}$

3. g is an example of a step function. Why do you think it is called a step function?

   Hint (c):

   The shape of the graph should help answer this question.

   Use the eTool below to examine the graph of $g(x)$.
   Click the link at right for the full version of the eTool: Calc 1-20 HW eTool