### Home > PC3 > Chapter 3 > Lesson 3.1.5 > Problem3-83

3-83.

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.

2. The function, $g$, is an example of a step function. Why do you think it is called a step function?
$5(2)+3(1)+8(4)$