Chapter 2, Problem 1MCCP

In Exercises 1-6, determine whether each relation is a function. Give the domain and range for each relation.

$\{(2,6),(1,4),(2,-6)\}$

To determine

Whether each relation is a function and provide the domain and range for the relation $\left\{\left(2,6\right),\left(1,4\right),\left(2,-6\right)\right\}$.

Answer to Problem 1MCCP

Solution: The relation is not a function.

The domain is $\underset{\_}{\left\{1,2\right\}}$.

The range is $\underset{\_}{\left\{-6,4,6\right\}}$

Explanation of Solution

Given: $\left\{\left(2,6\right),\left(1,4\right),\left(2,-6\right)\right\}$

Explanation:

A function is a correspondence from a first set, called the domain, to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range.

The domain is $\underset{\_}{\left\{1,2\right\}}$.

The range is $\underset{\_}{\left\{-6,4,6\right\}}$

Here in the domain element $2$ corresponds to $6$ in the range. But element 2 also corresponds to $-6$. Each element does not correspond to exactly one element in the range. So, the relation is not a function.