Are two circles that are labeled Domain and Range with the numbers 3,6,8,11 in the Domain circle and the numbers 4,5,7 in the Range circle these numbers are right across from each other with a arrow going from 3 to 4 and arrow going from 6 to 5, and arrow going from 11 to 7 across from the number 8 it is blank. Is this considered a function?

Answer 1

To determine if the relation you've described is a function, we need to refer to the definition of a function in mathematics: a relation is a function if every element in the domain is related to exactly one element in the range.

Let's break down the elements you've provided:

Domain:

• 3
• 6
• 8
• 11

Range:

• 4
• 5
• 7

Mappings:

• 3 → 4
• 6 → 5
• 11 → 7
• 8 → (no mapping, left blank)

Now, the key points to evaluate:

1. Each number in the Domain must relate to exactly one number in the Range.
2. The number 8 does not have any corresponding number in the Range, meaning it has no mapping.

Since 8 is in the Domain but does not map to any number in the Range, the relation does not satisfy the definition of a function. In a function, every element in the Domain must be associated with exactly one element in the Range.

Therefore, this relation is not considered a function.