Question

Use the set of ordered pairs to

(i) determine whether the relation is a function

(ii) find the domain of the relation

(iii) find the range of the function.

a. $\left\{\left(-3-6\right),\left(-2,-4\right),\left(-1,-2\right),\left(0,0\right),\left(1,2\right),\left(2,4\right),\left(3,6\right)\right\}$

b.$\left\{\left(8,-4\right),\left(4,-2\right),\left(2,-1\right),\left(0,0\right),\left(2,1\right),\left(4,2\right),\left(8,4\right)\right\}$

Short answer

a. Each x-value is matched with only one y-value. So this relation is a function.

b. Each x-value is matched with more than one y-value. So this relation is not a function.

Step-by-step solution

Given data

$\left\{\left(-3-6\right),\left(-2,-4\right),\left(-1,-2\right),\left(0,0\right),\left(1,2\right),\left(2,4\right),\left(3,6\right)\right\}$

Part(i)

Each x-value is matched with only one y-value. So this relation is a function.

Part(ii)

The domain is the set of all x-values in the relation.

The domain is:$\left\{-3,-2,-1,0,1,2,3\right\}$

Part(iii)

The range is the set of all y-values in the relation.

The range is:$\left\{-6,-4,-2,0,2,4,6\right\}$

Given data

$\left\{\left(8,-4\right),\left(4,-2\right),\left(2,-1\right),\left(0,0\right),\left(2,1\right),\left(4,2\right),\left(8,4\right)\right\}$

Part(i)

The x-value $4$and $8$ are matched with two y-values. So, this relation is not a function.

Part(ii)

The domain is the set of all x-values in the relation.

The domain is:

$\left\{8,4,2,0\right\}$

Part(iii)

The range is the set of all y-values in the relation.

The range is:

$\left\{-4,-2,-1,0,1,2,4\right\}$