Chapter 4.7, Problem 34E

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.

  $f(x)=\{\begin{array}{l}-2if-6\le x<-5\\ -1if-5\le x<-3\\ 0if-3\le x<-2\\ 1if-2\le x<0\end{array}$

Graph: In graph gap between two vertical lines and two horizontal lines is 1unit.

  

Interpretation: Observe the graph carefully, at $x=-6$ value is $-2$ , and in between $-6\le x<-5$ value is $-2$ .and in between $-5\le x<-3$ value is $-1$ .and in between $-3\le x<-2$ value is $0$ .and in between $-2\le x<0$ value is $1$ .Hence domain(expansion of graph in $x-axis$ ) is $x\in [-6,0)$ .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 $\{-2,-1,0,1\}$ .