Q1. - Algebra 2

Question

Write a relation of four ordered pairs that is not a function.

Step-by-Step Solution

Answer

The required relation is $R=\left\{\left(-1,2\right),\left(0,3\right),\left(0,5\right),\left(1,4\right)\right\}$.

Step 1 – Definition of function.

A relation is a function if each element of the domain is paired with exactly one element of the range.

A relation is not a function if there exist an element in the domain paired with more than one element of the range.

Step 2 – Given information.

The relation contains four ordered pairs and the relation is not a function.

Step 3 – Write the required relation.

The relation is not a function it means there exist at least two ordered pairs in which the x-coordinate are the same and the y-coordinates are different.

Let a relation of four ordered pairs.

$R=\left\{\left(-1,2\right),\left(0,3\right),\left(0,5\right),\left(1,4\right)\right\}$

This relation is not a function because 0 in the domain is paired with both 3 and 5 in the range.

Thus, the required relation is $R=\left\{\left(-1,2\right),\left(0,3\right),\left(0,5\right),\left(1,4\right)\right\}$.