Chapter 9.1, Problem 28IP

(a)

To determine

To write: The values in the table as a set of ordered pairs. Also explain if the data represents a function.

Answer to Problem 28IP

The values in the table are represented as a set of ordered pairs as follows:

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

This relation represents a function.

Explanation of Solution

Given information:

The following table:

The values in the table are represented as a set of ordered pairs as follows:

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

The above relation is a function because each domain value is paired with exactly one range value. If any of the domain values were paired with more than one range values, the given relation would not have qualified as a function.

(b)

To determine

To write: Inverse of the ordered pairs of the given data. Also, explain if the obtained data represents a function.

Answer to Problem 28IP

Inverse of the ordered pairs are represented as follows:

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

This relation does not represent a function.

Explanation of Solution

Given information:

The following table:

Inverse of the ordered pairs are represented as follows:

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

The above relation is not a function because $34$ in the domain value is paired with two range values, $1990$ and $2000$ . If each domain value was paired with exactly one range value, the given relation would have qualified as a function.