Chapter 8.1, Problem 37PPS

(a)

To determine

To calculate: To write the values in the table as a set of ordered pairs and find if data represent a function.

Answer to Problem 37PPS

The set of ordered pairs is a function

Explanation of Solution

Given information: Table showing the average number of hours worked weekly by U.S production workers for various years

Year	Hours
1970	37
1980	35
1990	34
2000	34

Formula Used:

According to function rule, no input can have more than one output.

The set ordered pairs is referred to as function when no two ordered pairs have the same first coordinate with different second coordinate

Calculation:

Given the table showing the average number of hours worked weekly by U.S production workers for various years

Year	Hours
1970	37
1980	35
1990	34
2000	34

Set of ordered pairs of is represented as below

  $\left\{\left(1970,37\right),\left(1980,35\right),\left(1990,34\right),\left(2000,34\right)\right\}$

Here, no two ordered pairs have same first coordinate.

Thus, the set of ordered pairs is a function

Conclusion:

Hence, the set of ordered pairs is a function

(b)

To determine

To calculate: To write the inverse of the ordered pairs of the data and find if the data represents a function

Answer to Problem 37PPS

The inverse of the data is NOT a function

Explanation of Solution

Given information: Table showing the average number of hours worked weekly by U.S production workers for various years

Year	Hours
1970	37
1980	35
1990	34
2000	34

Formula Used:

According to function rule, no input can have more than one output.

The set ordered pairs is referred to as function when no two ordered pairs have the same first coordinate with different second coordinate

Calculation:

Given the table showing the average number of hours worked weekly by U.S production workers for various years

Year	Hours
1970	37
1980	35
1990	34
2000	34

Given that inverse of a relation is obtained by switching the order of the number in each ordered pair

Set of ordered pairs of is represented as below

  $\left\{\left(1970,37\right),\left(1980,35\right),\left(1990,34\right),\left(2000,34\right)\right\}$

Inverse of the relation is given as

  $\left\{\left(37,1970\right),\left(35,1980\right),\left(34,1990\right),\left(34,2000\right)\right\}$

Consider $\left(34,1990\right),\left(34,2000\right)$ from the above set of ordered pairs

Here, the ordered pairs have same first coordinate.

Thus, the set of ordered pairs is NOT a function

Conclusion:

Hence, the set of ordered pairs is NOT a function