Let $g ( x ) = \left\{ \begin{array} { l l l } { 5 } & { \text { if } } & { 2 \leq x \leq 4 } \\ { 3 } & { \text { if } } & { 4 < x \leq 5 } \\ { 8 } & { \text { if } } & { 5 < x \leq 9 } \end{array} \right.$. 

1. Sketch the graph of $y=g(x)$ and shade the area between $y=g(x)$ and the $x$-axis.

   Hint (a):

   Your shaded region should be a set of rectangles.

2. The function, $g$, is an example of a step function. Why do you think it is called a step function?

3. Calculate the area of the shaded region.

   Step (c):

   $5(2)+3(1)+8(4)$