Question

fill in the blanks below in order to justify whether or not the mapping shown represents a function.

the mapping diagram above does not represent a function since dropdown in dropdown where there dropdown.

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 \(-1\): Mapped to \(3\) (one mapping).
• Element \(4\): Mapped to \(-3\) (one mapping).
• Element \(-2\): Mapped to \(8\) and \(5\) (two mappings).

Step3: Determine if function

Since \(-2\) in Set A is mapped to two elements (\(8\) and \(5\)) in Set B, it violates the function definition (each domain element must have exactly one codomain element).

Answer:

The mapping diagram above \(\boldsymbol{\text{does NOT represent}}\) a function since \(\boldsymbol{-2}\) in \(\boldsymbol{\text{Set A}}\) where there \(\boldsymbol{\text{is more than one number}}\) in \(\boldsymbol{\text{Set B}}\) assigned to it (instead of for each number in Set A there is one number in Set B).