Question

Determine if the relation below is a function and state the domain and range.

Answer 1

Please check the explanation.

Explanation:

Given the relation

{(1, -2), (-2, 0), (-1, 2), (1, 3)}

Please note that there is a repetition of x-values.

i.e. x=1 appears twice times.

This relation does not define a function because every x-value should have been unique and is associated with only one value of y.

Here, the x-values are repeated. Hence, this relation is not a function.

Finding the Domain of a relation:

We know that the domain is the complete set of all first elements of ordered pairs often called x-coordinates.

Domain of a relation: {-1, -2, 1}

Note: Domain is in ascending order and repeated elements are written only once.

Finding the Range of a relation:

We know that the domain is the complete set of all second elements of ordered pairs often called y-coordinates.

Range of a relation: {-2, 2, 3}

Note: Range is in ascending order and repeated elements are written only once.