Chapter 4.6, Problem 1P

a.

To determine

The domain and range of given relation and whether the given relation is a function or not by using a mapping diagram.

Answer to Problem 1P

The domain is $\left\{4.2,5,7,4.2\right\}$ .

The range is $\left\{1.5,2.2,4.8,0\right\}$ .

The given relation is not a function.

Explanation of Solution

Given: $\left\{\left(4.2,1.5\right),\left(5,2.2\right),\left(7,4.8\right),\left(4.2,0\right)\right\}$

The domain is $\left\{4.2,5,7\right\}$ .

The range is $\left\{1.5,2.2,4.8,0\right\}$ .

Mapping diagram

  

The domain value 4.2 is mapped to two range values. The relation is not a function.

b.

To determine

The domain and range of given relation and whether the given relation is a function or not by using a mapping diagram.

Answer to Problem 1P

The domain is $\left\{-1,-2,4,7\right\}$ .

The range is $\left\{1,2,-4,-7\right\}$ .

The given relation is a function.

Explanation of Solution

Given: $\left\{\left(-1,1\right),\left(-2,2\right),\left(4,-4\right),\left(7,-7\right)\right\}$

The domain is $\left\{-1,-2,4,7\right\}$ .

The range is $\left\{1,2,-4,-7\right\}$ .

Mapping diagram

  

Each domain value is mapped to only one range value. The relation is a function.