Chapter 4, Problem 1CT

To determine

Graph the function .Describe the domain and range.

Answer to Problem 1CT

Domain—Set of all real numbers.

Range-----Set of all real numbers.

Explanation of Solution

Given information: $y=2x+4\text{if}x\le -1\text{and}y=(1/3)x-1i\text{f}x>-1.$

Calculation:

When $x\le -1\text{then}y=2x+4.$ ….(1)

Putting $x=-1\text{then}y=2\times (-1)+4=-2+4=2.$

Putting $x=-2\text{then}y=2\times (-2)+4=-4+4=0.$

Putting $x=-3\text{then}y=2\times (-3)+4=--6+4=-2.$

When $x>-1\text{then}y=(1/3)x-1.$ ….(2)

Putting $x=0\text{then}y=(1/3)\times 0-1=0-1=-1.$

Putting $x=1\text{then}y=(1/3)\times 1-1=(1/3)-1=-2/3.$

Putting $x=2\text{then}y=(1/3)\times 2-1=(2/3)-1=-1/3.$

Putting $x=3\text{then}y=(1/3)\times 3-1=1-1=0.$

$x$	$y$
-1	2
-2	0
-3	-2
0	-1
1	-2/3
2	-1/3
3	0

The graph from the table is given below

  

Domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis. So the domain of the above graph is $x\le -1\text{and}x>-1$ that is set of all real numbers and for every real value of x there is a real value of y .

Domain—Set of all real numbers.

Range-----Set of all real numbers.