Question

fill in the blanks below in order to justify whether or not the mapping shown represents a function. set a set b -2 2 -3 -4 4 7 0

Explanation:

Step1: Recall Function Definition

A function is a relation where each element in the domain (Set A) is mapped to exactly one element in the codomain (Set B).

Step2: Analyze Set A Elements

• Element \(-2\) in Set A: It has multiple arrows (mappings) to different elements in Set B (e.g., \(-4\), \(0\), maybe others).
• Element \(-3\): Also has multiple mappings (to \(7\), \(0\), etc.).
• Element \(4\): Has multiple mappings (to \(7\), \(0\), etc.).

Since at least one element in Set A (domain) is mapped to more than one element in Set B (codomain), the mapping does not satisfy the definition of a function.

Answer:

The mapping does not represent a function because at least one element in Set A (e.g., \(-2\), \(-3\), \(4\)) is mapped to more than one element in Set B, violating the definition of a function (each domain element must map to exactly one codomain element).