Chapter 4.7, Problem 4CYU

To determine

To Graph:

Graph the step function based on the values given in the table.

Explanation of Solution

Given Information:

Elan is ordering a gift for his dad online. The table shows shipping rates . Graph the step function.

  

Concept Used :

1.Step Function:

The graph of a step function is a series of line segments .Because each part of a step function is linear , this type of function is called a piecewise-linear function.

2.For the interval $I=(a,b]=\{x:a<x\le b\}$ we have that the point a is not included and showed on graph with open circle; and point b is included and showed on graph with closed circle.

Graph :

We can represent the table values as a function :

  $f(x)=\{\begin{array}{l}3.99if0<x\le 15\\ 5.99if15<x\le 30\\ 6.99if30<x\le 50\\ 7.99if50<x\le 75\\ 8.99if75<x\le 100\\ 9.99if100<x\end{array}$

Graph the order total t on the x -axis and the shipping cost C on the y -axis.

If

  $\begin{array}{l}0<t\le 15\\ then\\ C=3.99\end{array}$

So, there is and open circle at (0,3.99) and a closed circle at (15,3.99).Connect these points with a line .Graph the rest of the data in the table similarly.