Q19. - Algebra 1

Question

Determine whether the relation $\left\{\left(2,3\right),\left(-1,3\right),\left(0,4\right),\left(3,2\right),\left(-2,3\right)\right\}$ is a function.

Step-by-Step Solution

Answer

The relation $\left\{\left(2,3\right),\left(-1,3\right),\left(0,4\right),\left(3,2\right),\left(-2,3\right)\right\}$ is a function.

Step 1. Given information.

We have a relation $\left\{\left(2,3\right),\left(-1,3\right),\left(0,4\right),\left(3,2\right),\left(-2,3\right)\right\}$

To show that this relation is a function or not.

Step 2. Concept apply.

We said any relation is a function, if each different first element is associated with a unique different second element in its all given ordered pairs. 

Step 3. Calculation.

In the given relation each first value of the ordered pair is associated with a unique second value of the given ordered pair.

As 2 is associated with 3, $-1$ is associated with 3, 0 with 4, 3 with 2 and $-2$ is associated with 3.

Hence, the given relation is a function.