Chapter 4.7, Problem 19E

To determine

Graph the function. Describe the domain and range..

Answer to Problem 19E

The domain is all real number.

The range is $(-\infty ,2]$ .

Explanation of Solution

Given information: The function $y=\{\begin{array}{l}1,\mathrm{if}x<-3\\ x-1,\mathrm{if}-3\le x\le 3\\ -2x+4,\mathrm{if}x>3\end{array}$ .

Calculation: The given function:

  $y=\{\begin{array}{l}1,\mathrm{if}x<-3\\ x-1,\mathrm{if}-3\le x\le 3\\ -2x+4,\mathrm{if}x>3\end{array}$ .

Graph $y=1\mathrm{for}x<2$ .Because $x$ is not equal to $-3$ ,we use an open circle at $(-3,1)$ .

Then we graph $x-1\mathrm{for}-3\le x\le 2$ .Because x is greater than or equal to $-3$ and smaller than or equal to $3$ ,we use closed circle at $(-3,-4)\mathrm{and}(3,2)$ .

Finally we graph $-2x+4\mathrm{for}x>3$ .Because $x$ is not equal to $3$ , we use an open circle at $(3,-2)$ .

  

Therefore the domain is all real number.

The range is $(-\infty ,2]$ .