Chapter 1.1, Problem 16CFU

a.

To determine

To find: the set of ordered pairs, the domain and range of the relation.

Answer to Problem 16CFU

Ordered pair = $\left\{\begin{array}{l}\left(83,240\right),\left(81,220\right),\left(82,245\right),\left(78,200\right),\left(83,255\right),\left(73,200\right),\left(80,215\right),\\ \left(77,210\right),\left(78,190\right),\left(73,180\right),\left(86,300\right),\left(77,220\right),\left(82,260\right)\end{array}\right\}$

Domain = $\left\{73,77,78,80,81,82,83,86\right\}$

Range = $\left\{180,190,200,210,215,220,240,245,255,260,300\right\}$

Explanation of Solution

Given information:

The given details are as follows:

Height (in)	Weight (lb)
83	240
81	220
82	245
78	200
83	255
73	200
80	215
77	210
78	190
73	180
86	300
77	220
82	260

Let the height be x and weight be y.

Calculation:

From the table, the set of ordered pairs of the relation in (x,y) is as follows:

  $\left\{\begin{array}{l}\left(83,240\right),\left(81,220\right),\left(82,245\right),\left(78,200\right),\left(83,255\right),\left(73,200\right),\left(80,215\right),\\ \left(77,210\right),\left(78,190\right),\left(73,180\right),\left(86,300\right),\left(77,220\right),\left(82,260\right)\end{array}\right\}$

Since all the possible values of x is a domain. So, domain value is as follows:

  $\left\{73,77,78,80,81,82,83,86\right\}$ .

All the possible values of yrepresent the range. So, the range is as follows:

  $\left\{180,190,200,210,215,220,240,245,255,260,300\right\}$ .

b.

To determine

To represent: the graph relation.

Answer to Problem 16CFU

  

Explanation of Solution

Given information:

The given details are as follows:

Height (in)	Weight (lb)
83	240
81	220
82	245
78	200
83	255
73	200
80	215
77	210
78	190
73	180
86	300
77	220
82	260

Let the height be x and weight be y.

Calculation:

Plot the values of (x,y) in the graph as follows:

  

c.

To determine

whether the relation is a function.

Answer to Problem 16CFU

Relation is not a function.

Explanation of Solution

Given information:

The given details are as follows:

Height (in)	Weight (lb)
83	240
81	220
82	245
78	200
83	255
73	200
80	215
77	210
78	190
73	180
86	300
77	220
82	260

Let the height be x and weight be y.

Calculation:

The relation is graphed as follows:

  

By looking at the graph or at the table, we find that there are more than one value of y for a particular value of x. Example, for height 73 inches, the possible weights are 180 and 200.

So, it fails the vertical line test and hence this relation is not a function.