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

To determine whether the relation $\left[\left(2,6\right),\left(1,4\right),\left(2,-6\right)\right]$ is a function or not.

Answer to Problem 1MCCP

Solution: No. The domain is $\underset{\_}{\left\{1,2\right\}}$ and the range is $\underset{\_}{\left\{-6,4,6\right\}}$.

Explanation of Solution

Given: The relation $\left[\left(2,6\right),\left(1,4\right),\left(2,-6\right)\right]$.

The relation is said to be a function if every element in the domain corresponds to exactly one element in the range.

The element $2$ in the domain corresponds to element $6$ in the range.

Furthermore, the element $1$ in the domain corresponds to element $4$ in the range and the element $2$ in the domain corresponds to element $-6$ in the range.

Here, two ordered pairs in the given relation have the same first component correspond to different elements.

Hence, the given relation is not a function.

Further, the domain is the set of all first components. Thus, the domain is $\left\{1,2\right\}$.

The range is the set of all second components. Thus, the range is $\left\{-6,4,6\right\}.$

Conclusion: The given relation is not a function. The domain is $\underset{\_}{\left\{1,2\right\}}$ and the range is $\underset{\_}{\left\{-6,4,6\right\}}$.