Use the domain and range of each of the following relations to determine which is a function.

Option A is correct.

{(3, -3), (9, -6) ,(0, -9)}

Step-by-step explanation:

A function is a relation in which every element of the domain is paired with exactly one element of the range.

(a)

{(3, -3), (9, -6) ,(0, -9)}

Domain is all the x-values, and range is all the y-values.

Domain: {3, 9, 0}

Range: {-3, -6, -9}

by definition;

each domain value is paired with exactly one element of range

⇒The given relation {(3, -3), (9, -6) ,(0, -9)} is a function.

(b)

{(3, -3), (9, -6) ,(3, -9)}

Domain is all the x-values, and range is all the y-values.

Domain: {3, 9, 3}

Range: {-3, -6, -9}

since, a function is a relation in which each domain value is paired with exactly one element of range.

In the domain , the value 3 is paired with -3 and -9

⇒the relation {(3, -3), (9, -6) ,(3, -9)} is not a function.

(c)

{(3, -3), (9, -6) ,(9,2), (0, -9)}

Domain is all the x-values, and range is all the y-values.

Domain: {3, 9, 9, 0}

Range: {-3, -6, 2, -9}

In the domain , the value 9 is paired with -3 and -9

⇒the relation {(3, -3), (9, -6) ,(9,2), (0, -9)} is not a function.

(d)

{3, 9, 0, -4}

Since, this does not contains any domain and range values.

therefore, this set is not a function.

amount of apples bought =$ 2.6

amount of peaches bought =$ 1.475

amount given by you to cashier= $ 20

amount received by me= amount given by you to cashier -   [amount of apples bought +amount of peaches bought]

                                        = 20   - [1.475 + 2.6]

                                        = 20 -   [ 4.075]

                                        =   $15.925

so, change received by me = $15.925