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. $\left\{\left(27,-3\right),\left(8,-2\right),\left(1,-1\right),\left(0,0\right),\left(1,1\right),\left(8,2\right),\left(27,3\right)\right\}$

b.role="math" localid="1644487005030" $\left\{\left(7,-3\right),\left(-5,-4\right),\left(8,-0\right),\left(0,0\right),\left(-6,4\right),\left(-2,2\right),\left(-1,3\right)\right\}$

Short answer

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

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

Step-by-step solution

Given data

$\left\{\left(27,-3\right),\left(8,-2\right),\left(1,-1\right),\left(0,0\right),\left(1,1\right),\left(8,2\right),\left(27,3\right)\right\}$

Part(i)

The x-value $27,8$and$1$arematched with more than one y-value.

So, this relation is not a function.

Part(ii)

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

The domain is:

$\left\{27,8,1,0\right\}$

Part(iii)

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

The range is:

$\left\{-3,-2,-1,0,1,2,3\right\}$

Given data

$\left\{\left(7,-3\right),\left(-5,-4\right),\left(8,-0\right),\left(0,0\right),\left(-6,4\right),\left(-2,2\right),\left(-1,3\right)\right\}$

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:

$\left\{7,-5,8,0,-6,-2,-1\right\}$

Part(iii)

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

The range is:

$\left\{-3,-4,-0,0,4,2,3\right\}$