Chapter 3.7, Problem 40HP

To determine

To draw: The graphs of step and piecewise functions and write a discussion of domains, ranges, maxima and minima.

Answer to Problem 40HP

For step function:

  $\text{Domain}=\text{All}\text{positive}\text{real}\text{numbers}$

  $\text{Range}=\{10,22,45\}$

Neither maximum nor minimum

For Piecewise function:

  $\text{Domain}=(-\infty ,0]\cup [2,\infty )$

  $\text{Range}=\text{All}\text{real}\text{numbers}\text{except}\text{on}\text{the}\text{interval}\text{of}(-3,5)$

Neither maximum nor minimum

Explanation of Solution

Given information: Step linear function $y=\left\{\begin{array}{l}10\text{if}0<x\le 8\\ 22\text{if}8<x\le 25\\ 45\text{if}x>25\end{array}\right\}$ and piecewise linear functions $y=\left\{\begin{array}{l}x-5\text{if}x\ge 2\\ x+5\text{if}x\le 0\end{array}\right\}$

Graph : Following is the graph of two given functions

  

From the graph we can see the both piecewise linear function as well as step linear function. In step function we can see finite no. of pieces in the given intervals on the other hand piecewise linear function shows different function with different intervals.