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.

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.