# Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 180: 127

One sample relation is: $\left( 2,0 \right)\text{ and }\left( 3,0 \right)$. (Many other examples are possible.)

#### Work Step by Step

The ordered pairs $\left( 2,0 \right)\text{ and }\left( 3,0 \right)$ are a set of 2 ordered pairs that are a relation and a function. $\left\{ 2,3 \right\}$ is the domain and $\left\{ 0 \right\}$ is the range. $\left\{ 2,3 \right\}$ are the values of the function from some set “A”, which is related to all the elements of some set B. So, if the digits of the ordered pairs are reversed, then the relation becomes $\left( 0,2 \right)\text{ and }\left( 0,3 \right)$. Now in this case, the domain of the set of ordered pairs will be $\left\{ 0 \right\}$ and its range will be $\left\{ 2,3 \right\}$. So the same element of set A has two images in the set B. This means that the relation violates the definition of the function. So, the set of ordered pairs $\left( 2,0 \right)\text{ and }\left( 3,0 \right)$ are a relation as well a function, but when the ordered pairs are reversed, then the relation obtained is not a function.

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