Question

for each relation, decide whether or not it is a function.

part 1 of 2

relation 1
{(-3, 6), (-7, 0), (-7, 6), (2, 6)}
function
not a function

part 2 of 2

relation 2
{(8, 6), (8, 7), (7, 7), (5, 7)}
function
not a function

Explanation:

Step1: Recall Function Definition

A relation is a function if each input (x - value) has exactly one output (y - value). So we check the x - values in each relation.

Step2: Analyze Relation 1

The relation is \(\{(-3,6),(-7,0),(-7,6),(2,6)\}\). The x - value \(-7\) is paired with two different y - values (\(0\) and \(6\)). So it does not satisfy the function definition.

Step3: Analyze Relation 2 (assuming the relation is \(\{(8,6),(8,7),(7,7),(5,7)\}\))

The x - value \(8\) is paired with two different y - values (\(6\) and \(7\)). So it also does not satisfy the function definition.

Answer:

• Relation 1: Not a Function (because the input \(-7\) has more than one output)
• Relation 2: Not a Function (because the input \(8\) has more than one output)