Chapter 4.7, Problem 33E

To determine

To graph: Draw the graph of step function, find domain and range.

Explanation of Solution

Given information: In the question, step function is given. We will draw the graph, and through graph we can judge domain and range of the function.

  $f(x)=\{\begin{array}{l}\text{9 }if1<x\le 2\\ \text{6 }if\text{ 2<}x\le 4\\ \text{5 }if\text{ 4}<x\le 9\\ 1if\text{ 9<}x\le 12\end{array}$

Graph:

  

Interpretation: Observe the graph carefully, at $x=2$ value is $\text{9}$ , and in between $1<x\le 2$ value is $\text{9}$ .and in between $\text{2<}x\le 4$ value is $\text{6}$ And in between $\text{4}<x\le 9$ value is $\text{5}$ .And in between $\text{9<}x\le 12$ value is $1$ .Hence domain (expansion of graph in $x-axis$ ) is $x\in (1,12]$ .And Range is expansion of graph in $y-axis$ , $y$ value, image of domain. Here function is step. Hence range is $y$ value. Range is $\{1,5,6,9\}$ .